Optical system and method

ABSTRACT

An optical system comprising: an illumination system configured, to form a periodic illumination mode comprising radiation in a pupil plane of the optical system having a spatial intensity profile which is periodic in at least one direction, a measurement system configured to measure a dose of radiation which is received in an field plane of the optical system as a function of position in the field plane, and a controller configured to: select one or more spatial frequencies in the field plane at which variation in the received dose of radiation as a function of position is caused by speckle, and determine a measure of the variation of the received dose of radiation as a function of position at the selected one or more spatial frequencies, the measure of the variation in the received dose being indicative of speckle in the field plane.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority of EP application 15201057.5 which wasfiled on 18 Dec. 2015 and which is incorporated herein in its entiretyby reference.

FIELD

The present invention relates to an optical system and methods ofperforming measurements. The optical system may particularly, but notexclusively, form part of a lithographic apparatus.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a target portion of a substrate. A lithographic apparatus can beused, for example, in the manufacture of integrated circuits (ICs). Inthat circumstance, a patterning device, which is alternatively referredto as a mask or a reticle, may be used to generate a circuit patterncorresponding to an individual layer of the IC, and this pattern can beimaged onto a target portion (e.g. comprising part of, one or severaldies) on a substrate (e.g. a silicon wafer) that has a layer ofradiation-sensitive material (resist). In general, a single substratewill contain a network of adjacent target portions that are successivelyexposed. Known lithographic apparatus include so-called steppers, inwhich each target portion is irradiated by exposing an entire patternonto the target portion in one go, and so-called scanners, in which eachtarget portion is irradiated by scanning the pattern through the beam ina given direction (the “scanning”-direction) while synchronouslyscanning the substrate parallel or anti parallel to this direction.

It may be desirable to measure one or more properties of radiation whichpropagates through a lithographic apparatus. It is desirable to provide,apparatus and methods which obviate or mitigate one or more of theproblems of the prior art, whether identified herein or elsewhere.

SUMMARY

According to a first aspect of the invention, there is provided Anoptical system comprising: an illumination system configured, to form aperiodic illumination mode comprising radiation in a pupil plane of theoptical system having a spatial intensity profile which is periodic inat least one direction; a measurement system configured to measure adose of radiation which is received in an field plane of the opticalsystem as a function of position in the field plane; and a controllerconfigured to: select one or more spatial frequencies in the field planeat which variation in the received dose of radiation as a function ofposition is caused by speckle; and determine a measure of the variationof the received dose of radiation as a function of position at theselected one or more spatial frequencies, the measure of the variationin the received dose being indicative of speckle in the field plane.

The periodic illumination mode formed by the illumination system servesto confine the effects of speckle to a limited number of spatialfrequencies in the field plane of the optical system. A variation in thedose of radiation received in the field plane may be analysed at one ormore spatial frequencies in the field plane at which variation in thereceived dose of radiation as a function of position is caused byspeckle. This may for example, correspond with a position in anautocorrelation function at which a local maximum is caused by speckle.Confining the effects of speckle to limited spatial frequenciesadvantageously allows the contribution of speckle to a dose variation inthe field plane to be separated from the contribution of other effects.

A field plane may be an image plane or an object plane of the opticalsystem. A pupil plane of an optical system is a plane which has aFourier relationship with a field plane. That is, each spatial point ina pupil plane corresponds with an angle in a corresponding field planeand vice versa.

The illumination system may be configured to illuminate a patterningdevice with a radiation beam, the patterning device being configured toimpart the radiation beam with a pattern in its cross-section so as toform a patterned radiation beam.

The optical system may further comprise a projection system configuredto project a radiation beam onto an field plane.

The radiation beam which is projected onto the field plane may, forexample, be a patterned radiation beam which is patterned by thepatterning device.

The controller may be further configured to determine the contributionof speckle to the variation in the received dose, the contribution ofspeckle being determined using the measure of the variation of thereceived dose at the selected one or more spatial frequencies.

The determined contribution of speckle to the variation in the receiveddose may comprise a variance of the dose which is caused by speckle.

The controller may be configured to determine, from the measure of thevariation of the received dose at the selected one or more spatialfrequencies, a number of independent speckle patterns which are receivedin the field plane in a given period of time.

The measurement system may comprise a substrate table configured to holda substrate substantially in the field plane so as to expose thesubstrate to the patterned radiation beam; and a sensor configured todetect a dimension of a feature patterned into the substrate atdifferent positions on the substrate, the dimension of the featurepatterned into the substrate as a function of position on the substrateproviding a measure of the dose of radiation received in the field planeas a function of position in the field plane.

The sensor may comprise a scanning electron microscope configured totake an image of the feature patterned onto the substrate and acontroller configured to detect, from the image, a dimension of thefeature at different positions on the substrate.

The measurement system may further comprise a track configured to applya resist to a substrate and develop the resist after exposure to apatterned radiation beam so as to transfer the pattern to the substrate.

The controller may be configured to determine an autocorrelationfunction of a first series and a second series, wherein the first seriescomprises the measured received dose of radiation in the field plane atdifferent positions in the field plane and the second series is the sameas the first series and offset from the first series by a positionaloffset.

The controller may be configured to evaluate the autocorrelationfunction at a positional offset which is the inverse of the one or moreselected spatial frequencies.

The positional offset which is the inverse of the one or more selectedspatial frequencies may represent a positional offset at which theautocorrelation function is substantially at a local maximum.

The autocorrelation function evaluated at a positional offset which isthe inverse of the one or more selected spatial frequencies may providea measure of the contribution of speckle to a variation in the receiveddose of radiation as a function of the position in the field plane.

The controller may be further configured to scale the autocorrelationfunction evaluated at a positional offset which is the inverse of theone or more selected spatial frequencies and determine the totalvariance in the received dose of radiation in the field plane which iscaused by speckle.

The controller may be further configured to: determine a ratio of alocal maximum to a global maximum in a speckle autocorrelation functionwhich corresponds to a variation in dose in the field plane which isonly caused by speckle; and scale the autocorrelation function evaluatedat a positional offset which is the inverse of the one or more selectedspatial frequencies according to the determined ratio.

The optical system may further comprise a sensor apparatus configured tomeasure the spatial intensity profile of the periodic illumination modein the pupil plane of the optical system, wherein the controller isconfigured to determine, from the measured spatial intensity profile ofthe periodic illumination mode, the ratio of a local maximum to a globalmaximum in a speckle autocorrelation function, wherein the speckleautocorrelation function corresponds to a variation in dose in the fieldplane which is only caused by speckle.

The controller may be configured to perform a simulation of radiationpropagating through the optical system and determine, from thesimulation, the ratio of a local maximum to a global maximum in aspeckle autocorrelation function which corresponds to a variation indose in the field plane which is only caused by speckle.

The optical system may further comprise a radiation source configured toprovide a radiation beam to the illumination system, wherein theradiation source is operable to adjust a property of the radiation beamso as to change a number of independent speckle patterns which arereceived in the field plane per unit time.

The radiation source may be configured to provide a pulsed radiationbeam to the illumination system and wherein the radiation source isoperable to adjust the duration of pulses of radiation which are emittedfrom the radiation source, thereby changing the number of independentspeckle patterns which are received in the field plane per unit time.

For each configuration of the adjustable property of the radiationsource, the controller is configured to: select one or more spatialfrequencies in the field plane at which variation in the received doseof radiation as a function of position is caused by speckle; anddetermine a measure of the variation of the received dose of radiationas a function of position at the selected one or more spatialfrequencies, the measure of the variation in the received dose beingindicative of speckle in the field plane.

The controller may be further configured to evaluate the measure of thevariation in the received dose at a plurality of configurations of theadjustable property of the radiation source, and from the evaluationdetermine the contribution of speckle to the variation of the receiveddose at each configuration.

The controller may be configured to select the one or more spatialfrequencies in the field plane at which the variation in the measureddimension is caused by speckle, using the number of periods of thespatial intensity distribution in the pupil plane of the optical system.

The controller may be configured to select the one or more spatialfrequencies in the field plane at which the variation in the measureddimension is caused by speckle by calculating a spatial period P_(S)according to:

$P_{S} = \frac{\lambda \; K}{2{NA}}$

where K is the number of periods of the spatial intensity distributionin the pupil plane of the optical system, λ is the wavelength of theradiation beam and NA is the numerical aperture of the optical system,wherein the one or more spatial frequencies in the field plane at whichthe variation in the measured dimension is caused by speckle is theinverse of the spatial period P_(S).

The illumination system may comprise an array of mirrors, the mirrorsbeing adjustable so as to adjust the spatial intensity profile in thepupil plane of the optical system.

The illumination system may be configured to form a periodicillumination mode comprising radiation in a pupil plane of the opticalsystem having a periodic spatial intensity profile in a first direction,wherein the periodic spatial intensity profile includes K periods.

The illumination system may be configured such that the spatialintensity profile substantially follows a Gaussian distribution in asecond direction, wherein the second direction is substantiallyperpendicular to the first direction.

K may be an integer.

K may be an odd number.

K may be 5 or more.

K may be 17 or less.

The illumination system may be configured to form a dipole illuminationmode

The optical system may comprise a lithographic apparatus.

The patterning device may be an attenuating phase shift mask

According to a second aspect of the invention there is provided a methodof measuring speckle in an optical system, the optical system comprisingan illumination system configured to condition a radiation beam, themethod comprising: configuring the illumination system to form aperiodic illumination mode, comprising radiation in a pupil plane of theoptical system having a spatial intensity profile which is periodic inat least one direction; measuring a dose of radiation which is receivedin an field plane of the optical system as a function of position in thefield plane; selecting one or more spatial frequencies in the fieldplane at which variation in the received dose of radiation as a functionof position is caused by speckle; and determining a measure of thevariation of the received dose of radiation as a function of position atthe selected one or more spatial frequencies, the measure of thevariation in the dimension being indicative of the speckle in the fieldplane.

According to a third aspect of the invention there is provided a methodof measuring speckle in a lithographic apparatus, the method comprisingforming a periodic illumination mode of radiation; patterning theradiation using a pattern comprising a grating; projecting the patternedradiation onto a substrate to form an image of the grating; measuringline width variation of lines of the imaged grating; and performing atwo-dimensional correlation of the line widths in which lines arecorrelated with themselves and are correlated with other lines of theimage

The method may further comprise determining a ratio of a local maximumto a central maximum for one or more lines which were correlated withother lines of the image, and using that ratio together with a localmaximum for lines which were correlated with themselves to determine acentral maximum caused by speckle for the lines which were correlatedwith themselves

The method may further comprise using a previously performed calibrationto convert the size of the central maximum to a measurement of dosevariation caused by speckle.

The method of the third aspect of the invention advantageously doesn'trequire a simulation of the effect of speckle, or a measurement of theintensity distribution of the illumination mode in a pupil plane.

According to a fourth aspect of the invention there is provided a methodof measuring speckle in a lithographic apparatus, the method comprisingforming a periodic illumination mode of radiation; patterning theradiation using a pattern comprising a grating; projecting the patternedradiation onto a substrate to form an image of the grating; measuringvariation of the positions of lines of the imaged grating; andperforming a two-dimensional correlation of the position variation inwhich lines are correlated with themselves and are correlated with otherlines of the image

According to a fifth aspect of the invention there is provided a methodof measuring speckle in a lithographic apparatus, the method comprisingforming a quadrupole illumination mode of radiation; patterning theradiation using a pattern comprising a two-dimensional array offeatures; projecting the patterned radiation onto a substrate to form animage; performing a two-dimensional correlation of the criticaldimension of the imaged pattern features as a function of patternfeature separation; determining a size of the correlation function awayfrom a central maximum of the correlation function, and using thistogether with a previously obtained ratio to determine the size of acentral maximum of the correlation function that is caused by speckle.

The method of the fifth aspect of the invention advantageously doesn'trequire a simulation of the effect of speckle, or a measurement of theintensity distribution of the illumination mode in a pupil plane.

According to a sixth aspect of the invention there is provided a methodof measuring speckle in a lithographic apparatus, the method comprisingforming a quadrupole illumination mode of radiation; patterning theradiation using a pattern comprising a two-dimensional array offeatures; projecting the patterned radiation onto a substrate to form animage; performing a two-dimensional correlation of the positions of theimaged pattern features as a function of pattern feature separation;determining a size of the correlation function away from a centralmaximum of the correlation function, and using this together with apreviously obtained ratio to determine the size of a central maximum ofthe correlation function that is caused by speckle.

The method of the sixth aspect of the invention advantageously doesn'trequire a simulation of the effect of, or a measurement of the intensitydistribution of the illumination mode in a pupil plane.

The method of the fifth aspect or the sixth aspect may further compriseusing a previously performed calibration to convert the size of thecentral maximum to a measurement of dose variation caused by speckle.

One or more aspects of the invention may include one or more features ofany of the other aspects of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in whichcorresponding reference symbols indicate corresponding parts, and inwhich:

FIG. 1 is a schematic illustration of a lithographic apparatus;

FIG. 2 is a representation of lithographic features which may be formedusing the lithographic apparatus of FIG. 1;

FIG. 3 is a representation of the power spectral density associated witha dimension of the lithographic features shown in FIG. 2;

FIG. 4 is a representation of an autocorrelation function associatedwith a dimension of the lithographic features shown in FIG. 2;

FIG. 5 is a representation of a spatial intensity profile of radiationin a pupil plane of an illumination system which forms part of thelithographic apparatus of FIG. 1;

FIG. 6 is a representation of an autocorrelation function associatedwith a dimension of a lithographic feature;

FIG. 7 is a representation of autocorrelation functions associated withdimensions of lithographic features formed using different illuminationmodes;

FIG. 8 is a representation of the position of local maxima in theautocorrelation functions of FIG. 7;

FIG. 9 is a representation of the height of local maxima in theautocorrelation functions of FIG. 7;

FIG. 10 is a representation of an autocorrelation function associatedwith a spatial intensity profile of radiation in a pupil plane of anillumination system;

FIG. 11 is a representation of the height of local maxima inautocorrelation functions associated with different spatial intensityprofiles of radiation in a pupil plane of an illumination system;

FIG. 12 is an illumination mode used by an embodiment of the invention;

FIG. 13 is a unit of a pattern used by an embodiment of the invention topattern radiation;

FIG. 14 is an image of lines formed using the illumination mode andpattern of FIGS. 12 and 13;

FIG. 15 is a graph obtained using a simulation which depicts standarddeviation of critical dimension and line position variation as afunction of 1/sqrt (number of independent speckle modes);

FIG. 16 is an image depicting a two-dimensional correlation of criticaldimension obtained from a simulation using the illumination mode andpattern of FIGS. 12 and 13;

FIG. 17 is a graph which depicts the measurement results of atwo-dimensional correlation between lines of the image of FIG. 14;

FIG. 18 is an illumination mode used by an embodiment of the invention;

FIG. 19 is a unit of a pattern used by an embodiment of the invention topattern radiation;

FIG. 20 is a graph obtained using a simulation which depicts standarddeviation of critical dimension and feature position variation as afunction of 1/sqrt(number of independent speckle modes);

FIG. 21 is an image depicting a two-dimensional correlation of criticaldimension obtained from a simulation using the illumination mode andpattern of FIGS. 18 and 19;

FIG. 22 is an image depicting a two-dimensional correlation ofy-direction position variation of features obtained from a simulationusing the illumination mode and pattern of FIGS. 18 and 19;

FIG. 23 is an image depicting a two-dimensional correlation ofx-direction position variation of features obtained from a simulationusing the illumination mode and pattern of FIGS. 18 and 19; and

FIG. 24 is a representation of steps of a method according to anembodiment of the invention.

DETAILED DESCRIPTION

Although specific reference may be made in this text to the use of alithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,liquid-crystal displays (LCDs), thin film magnetic heads, etc. Theskilled artisan will appreciate that, in the context of such alternativeapplications, any use of the terms “wafer” or “die” herein may beconsidered as synonymous with the more general terms “substrate” or“target portion”, respectively. The substrate referred to herein may beprocessed, before or after exposure, in for example a track (a tool thattypically applies a layer of resist to a substrate and develops theexposed resist) or a metrology or inspection tool. Where applicable, thedisclosure herein may be applied to such and other substrate processingtools. Further, the substrate may be processed more than once, forexample in order to create a multi-layer IC, so that the term substrateused herein may also refer to a substrate that already contains multipleprocessed layers. A substrate may be held by a substrate table.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of 365, 248, 193, 157 or 126 nm) and extremeultra-violet (EUV) radiation (e.g. having a wavelength in the range of4-20 nm), as well as particle beams, such as ion beams or electronbeams.

The term “patterning device” used herein should be broadly interpretedas referring to a device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate. Generally, the patternimparted to the radiation beam will correspond to a particularfunctional layer in a device being created in the target portion, suchas an integrated circuit.

A patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions; in this manner, thereflected beam is patterned.

A support structure may hold the patterning device. The way in which thesupport structure holds the patterning device may depend on theorientation of the patterning device, the design of the lithographicapparatus, and other conditions, such as for example whether or not thepatterning device is held in a vacuum environment. The support can usemechanical clamping, vacuum, or other clamping techniques, for exampleelectrostatic clamping under vacuum conditions. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired and which may ensure that the patterning device is at a desiredposition, for example with respect to the projection system. Any use ofthe terms “reticle” or “mask” herein may be considered synonymous withthe more general term “patterning device”.

The term “projection system” used herein should be broadly interpretedas encompassing various types of projection system, including refractiveoptical systems, reflective optical systems, and catadioptric opticalsystems, as appropriate for example for the exposure radiation beingused, or for other factors such as the use of an immersion fluid or theuse of a vacuum. Any use of the term “projection lens” herein may beconsidered as synonymous with the more general term “projection system”.

The term “illumination system” may also encompass various types ofoptical components, including refractive, reflective, and catadioptricoptical components for directing, shaping, or controlling the beam ofradiation, and such components may also be referred to below,collectively or singularly, as a “lens”.

A lithographic apparatus may be of a type having two (dual stage) ormore substrate tables (and/or two or more support structures). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure.

A lithographic apparatus may also be of a type wherein the substrate isimmersed in a liquid having a relatively high refractive index, e.g.water, so as to fill a space between the final element of the projectionsystem and the substrate. Immersion techniques are well known in the artfor increasing the numerical aperture of projection systems.

FIG. 1 schematically depicts a lithographic apparatus according to aparticular embodiment of the invention. The apparatus comprises:

-   -   an illumination system (illuminator) IL to condition a beam PB        of radiation (e.g. UV radiation or EUV radiation).    -   a support structure MT to support a patterning device (e.g. a        mask) MA and connected to first positioning device PM to        accurately position the patterning device with respect to a        projection system PL;    -   a substrate table (e.g. a wafer table) WT for holding a        substrate (e.g. a resist coated wafer) W and connected to second        positioning device PW for accurately positioning the substrate        with respect to the projection system PL;    -   a projection system (e.g. a refractive projection lens) PL        configured to image a pattern imparted to the radiation beam PB        by patterning device MA onto a target portion C (e.g. comprising        one or more dies) of the substrate W; and    -   a controller CN configured to control one or more components of        the lithographic apparatus and/or to compute one or more        properties associated with the lithographic apparatus.

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above).

The illumination system IL receives a beam of radiation from a radiationsource SO. The source and the lithographic apparatus may be separateentities, for example when the source is an excimer laser. In suchcases, the source is not considered to form part of the lithographicapparatus and the radiation beam is passed from the source SO to theillumination system IL with the aid of a beam delivery system BDcomprising for example suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of theapparatus. The source SO and the illumination system IL, together withthe beam delivery system BD if required, may be referred to as aradiation system.

The illumination system IL may comprise adjusting means AM for adjustingthe angular intensity distribution of the beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illumination system can be adjusted. In addition, the illuminationsystem IL generally comprises various other components, such as anintegrator IN and a condenser CO. The illumination system provides aconditioned beam of radiation PB, having a desired uniformity andintensity distribution in its cross section.

The radiation beam PB is incident on the patterning device (e.g. mask)MA, which is held on the support structure MT. Having traversed thepatterning device MA, the beam PB passes through the projection systemPL, which focuses the beam onto a target portion C of the substrate W.With the aid of the second positioning device PW and position sensor IF(e.g. an interferometric device), the substrate table WT can be movedaccurately, e.g. so as to position different target portions C in thepath of the beam PB. Similarly, the first positioning device PM andanother position sensor (which is not explicitly depicted in FIG. 1) canbe used to accurately position the patterning device MA with respect tothe path of the beam PB, e.g. after mechanical retrieval from a masklibrary, or during a scan. In general, movement of the object tables MTand WT will be realized with the aid of a long-stroke module (coarsepositioning) and a short-stroke module (fine positioning), which formpart of the positioning device PM and PW. However, in the case of astepper (as opposed to a scanner) the support structure MT may beconnected to a short stroke actuator only, or may be fixed. Patterningdevice MA and substrate W may be aligned using patterning devicealignment marks M1, M2 and substrate alignment marks P1, P2.

The depicted apparatus can be used in the following preferred modes:

1. In step mode, the support structure MT and the substrate table WT arekept essentially stationary, while an entire pattern imparted to thebeam PB is projected onto a target portion C in one go (i.e. a singlestatic exposure). The substrate table WT is then shifted in the X and/orY direction so that a different target portion C can be exposed. In stepmode, the maximum size of the exposure field limits the size of thetarget portion C imaged in a single static exposure.2. In scan mode, the support structure MT and the substrate table WT arescanned synchronously while a pattern imparted to the beam PB isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the supportstructure MT is determined by the (de-)magnification and image reversalcharacteristics of the projection system PL. In scan mode, the maximumsize of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.3. In another mode, the support structure MT is kept essentiallystationary holding a programmable patterning device, and the substratetable WT is moved or scanned while a pattern imparted to the beam PB isprojected onto a target portion C. In this mode, generally a pulsedradiation source is employed and the programmable patterning device isupdated as required after each movement of the substrate table WT or inbetween successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

The radiation source SO may emit radiation which exhibits spatialcoherence having a coherence length and temporal coherence having acoherence time. For example, in embodiments in which the radiationsource SO comprises a laser (e.g. an excimer laser) the emitted laserbeam may exhibit spatial and temporal coherence. In the illuminationsystem IL and/or the projection system PS, radiation from differentparts of the radiation beam emitted from the radiation source SO may bemixed together. The spatial coherence of the radiation beam may causedifferent parts of the radiation beam which are mixed together tointerfere with each other, thereby forming an interference pattern. Inparticular an interference effect commonly known as speckle may occur.Speckle is a positional variation in the intensity of a radiation beamwhich results from mutual interference of a set of wavefronts. Forexample, radiation in an image plane of a lithographic apparatus mayinterfere. Consequently an interference pattern is formed in the imageplane. The interference pattern may be referred to as a speckle pattern.The substrate W is typically situated substantially in an image plane ofthe lithographic apparatus LA. A speckle pattern in the image plane willtherefore affect the spatial intensity profile of the radiation to whichthe substrate W is exposed.

During a lithographic process it is desirable to control a dose ofradiation which is received at different positions on a substrate W. Areceived dose of radiation at a given point on a substrate is anintegral of the intensity of radiation received at that point over thetime for which the point is exposed to radiation.

At a single point in time, different positions on the substrate W mayreceive different intensities of radiation due to static speckle (theinstantaneous speckle pattern). However, the speckle pattern may varywith time. The time scale over which the speckle pattern varies is thecoherence time of the radiation beam. If a region of the substrate isexposed to radiation for a period of time (an exposure time) which ismuch greater than the coherence time, then the speckle pattern willchange many times during the exposure time. This may smooth out theeffects of the speckle pattern over time and consequently speckle mayonly cause relatively small variations in the dose of radiation receivedat different positions across the exposed region of the substrate W.

However, if the exposure time is of the same order of or smaller thanthe coherence time then the speckle pattern may not change or may onlychange a few times during the exposure time. Consequently differentportions of the exposed region of the substrate W may receive differentdoses of radiation due to speckle.

In embodiments in which the radiation source SO provides a pulsedradiation beam, the coherence time of the radiation beam may be smallerthan the duration of a single pulse of the radiation beam. More than onespeckle pattern may therefore occur during a single pulse of theradiation beam. In some embodiments, the exposure period may includemultiple pulses of the radiation beam. This may serve to increase thetotal number of speckle patterns to which a given point on a substrateis exposed thereby temporally averaging out the effect of speckle whichis seen over the course of a single exposure period.

In some embodiments, a single pulse of radiation may include manyindependent speckle patterns. For example, the number of independentspeckle patterns in a single pulse of radiation may be greater than 10.In some embodiments the number of independent speckle patterns in asingle pulse of radiation may be about 25, about 50 or about 100 ormore.

References herein to an “exposure time” are intended to refer to thetotal amount of time for which a given point on a substrate is exposedto radiation. In embodiments in which a pulsed radiation source is used,the exposure time is equal to an integral over time of all the pulses ofradiation to which a given point on a substrate is exposed. The exposuretime does not include the time between radiation pulses.

References herein to an “exposure period” are intended to refer to atime period during which radiation (e.g. pulses of radiation) isreceived by a given point on a substrate. An exposure period may forexample, include a number of radiation pulses and includes the timeperiods between radiation pulses.

A positional variation in radiation dose across a substrate W may affectfeatures which are patterned onto the substrate W. For example thesubstrate W may be provided with a layer of resist (e.g. using a toolreferred to as a track). Regions of the resist are exposed to radiationduring a lithographic exposure, thereby causing a state change inexposed regions of the resist. The resist may then be developed byperforming an etching process so as to remove either the exposed regionsof the resist (which have undergone a state change) or the non-exposedregions of the resist (which have not undergone a state change). Etchingof some regions of the resist results in features being patterned intothe resist. The patterned features in the resist may form a mask forpatterning features into the substrate W, for example, by etchingportions of the substrate W from which the resist has been removed.

A dimension of a feature which is patterned into the resist andsubsequently into the substrate W, depends on the dose of radiationwhich is received by the resist (at the substrate W). For example, insome embodiments one or more line features may be patterned into theresist and subsequently onto the substrate W. A width W_(L) of the linefeature depends on the dose of radiation which is received at thesubstrate W. The width W_(L) of a lithographic feature may alternativelybe referred to as the critical dimension (CD) of the lithographicfeature.

In general two different types of resist may be used to form a patternon a substrate W. The two different types of resist may be referred toas a positive tone resist and a negative tone resist. A negative toneresist is configured to undergo a state change when exposed toradiation, such that exposed portions of the resist are resistant tobeing etched away during an etching process and thus remain on thesubstrate W. Portions of the resist which are not exposed to radiationare etched away during an etching process. When using a negative toneresist, an increase in the dose received at the substrate will increasethe width W_(L) of a line feature and a decrease in the received dosewill decrease the width W_(L) of the line feature.

A positive tone resist is configured to undergo a state change whenexposed to radiation, such that exposed portions of the resist areetched away during an etching process and are therefore removed from thesubstrate W. Portions of the resist which are not exposed to radiationare resistant to being etched away and thus remain on the substrate W.During an etching process it is therefore the portions of the resistwhich are exposed to radiation which are etched away during an etchingprocess. When using a positive tone resist, an increase in the dosereceived at the substrate W will decrease the line width W_(L) and adecrease in the received dose will increase the width W_(L) of the linefeature.

Methods which are described herein, seek to determine a dose ofradiation which is received at a substrate W as a function of positionon the substrate W. This may be achieved through use of either apositive tone resist or a negative tone resist, since when using bothforms of resist the line width WL depends on the dose of radiation whichis received. Measurements of the line width WL of exposed line featuresas a function of position along the line feature, may therefore be usedto determine the dose of radiation which is received at each positionalong the line feature.

As will be appreciated from the description above, a variation in thedose of radiation which is received at different positions on thesubstrate W (e.g. caused by speckle) may cause different positions alonga line feature to receive different doses of radiation. A variation inthe received dose along a line feature may lead to a variation in thewidth of the line feature at different positions along the line.Variations in the width of a line feature along the length of the linemay be referred to as line width roughness. Line width roughness is acommon measure used to characterize lithographic features. As wasexplained above, interference effects, in particular speckle, in alithographic apparatus LA may affect the line width roughness oflithographic features which are formed by the lithographic apparatus LA.

There is an increasing demand to reduce the size of lithographicfeatures (commonly referred to as a critical dimension). As the criticaldimension is decreased the effect of line width roughness becomes anincreasingly important factor and there is a desire to understand andquantify the contributions to line width roughness. In general there maybe many different effects which contribute to line width roughness andseparating these effects is difficult. In particular assessing thecontribution of speckle to line width roughness is made difficult by amultitude of stochastic effects which also contribute to line widthroughness. Other stochastic effects which contribute to line widthroughness may, for example, include effects related to chemical processwhich occur in a resist used during a lithographic exposure.

For some uses of a lithographic apparatus LA there may be a desire todecrease the bandwidth of the radiation which is provided by theradiation source SO and/or to decrease the number of pulses of radiationwhich are emitted from the radiation source SO during a single exposureperiod. Decreasing the bandwidth of radiation generally increases thecoherence length and the coherence time associated with the radiationand may therefore increase dose variations which are caused by speckle(the coherence time is equal to the coherence length divided by thespeed of light). Decreasing the number of pulses of radiation in anexposure period will decrease the total exposure time for which a givenpoint on the substrate W is exposed to radiation. This will decrease thenumber of independent speckle patterns which is seen by a given point onthe substrate and may therefore increase the influence of speckle on thedose of radiation which is received at the point on the substrate(assuming that the coherence time remains the same). The contribution ofspeckle to the line width roughness may therefore be particularlyimportant in situations in which reductions in the bandwidth and/or thenumber of pulses are contemplated.

In general, it is desirable to determine the effects of speckle in alithographic apparatus. For example, it may be desirable to determinethe contribution of speckle to a variation in a lithographic featurewhich is formed in a substrate W by a lithographic apparatus LA. Forexample, it may be desirable to determine the contribution of speckle toline width roughness of a line feature formed in a substrate W by alithographic apparatus LA.

Determining the effects of speckle in a lithographic apparatus LAadvantageously allows for a better understanding of the effects ofspeckle and allows speckle to be properly accounted for when selectingother properties of a lithographic apparatus LA. For example, anunderstanding of the effects of speckle may advantageously allow thebandwidth and/or the number of pulses (during an exposure period) ofradiation emitted from the radiation source SO to be selected whilstaccounting for the effects of speckle.

Speckle is often quantified using a speckle contrast C. The specklecontrast C is defined as the standard deviation a of radiation intensityacross an area divided by the mean radiation intensity Ī across the areaand may be given by equation (1).

$\begin{matrix}{C = {\frac{\sigma}{\overset{\_}{I}} = \frac{1}{\sqrt{N}}}} & (1)\end{matrix}$

Where N is the number of independent speckle patterns to which a givenpoint is exposed during a single exposure period. In embodiments inwhich the radiation SO comprises a laser which emits a laser beam, thenumber of independent speckle patterns N is equal to the number ofindependent laser modes with which the laser operates during a givenexposure period. The contribution of speckle to the line width roughnessdepends on the speckle contrast.

As was mentioned above determining the contribution of speckle tovariations in a lithographic feature (e.g. line width roughness) iscomplicated by other contributions, such as stochastic effects, whichalso cause variations in the lithographic feature. Embodiments of theinvention which are contemplated herein seek to separate thecontribution of speckle from other effects by confining the effects ofspeckle to limited spatial frequencies in an image plane (the plane inwhich a substrate to be exposed is substantially situated) of thelithographic apparatus LA.

Different spatial frequencies in an image plane of a lithographicapparatus may be analysed using signal processing analysis. One or moredimensions of a lithographic feature as a function of position may betreated as a series having different contributions at different spatialfrequencies. For example, the line width W_(L) of a line feature atdifferent positions along the line feature may be treated as a series.FIG. 2 is an image of lithographic line features 11 a, 11 b which areformed in a substrate W. The image which is shown in FIG. 2 was takenusing a scanning electron microscope. The edges of a first lithographicline feature 11 a and a second lithographic line feature 11 b have beendetected and are marked with solid lines in FIG. 2. Edges oflithographic features (such as the lithographic lines 11 a, 11 b) may bedetected using a suitable image processing technique.

Once the edges of the lithographic lines 11 a, 11 b are detected, thedistance between the detected edges may be determined. The distancebetween the detected edges is the line width and is labelled W_(L) inFIG. 2. As can be seen in FIG. 2 the line widths W_(L) of thelithographic line features vary as a function of position along anx-axis. The x-axis runs generally parallel to the direction in which thelithographic lines extend. The line width W_(L) of each line 11 a, 11 bat different x positions forms a series having different contributionsat different spatial frequencies.

FIG. 3 is a representation of an average power spectral density of aplurality of line width W_(L) series as a function of spatial frequency(in microns). The representation which is shown in FIG. 3 represents thecontributions at different spatial frequencies to the line width series,which are formed of line widths W_(L) at different x-positions. Thepower spectral density of the line width W_(L) series includes acontribution which is caused by speckle and a contribution which iscaused by effects other than speckle. Embodiments of the invention whichare contemplated herein seek to separate the contribution which iscaused by speckle from the other contribution so as to derive thevariation which is caused by speckle.

FIG. 4 is a representation of an autocorrelation function (expressed asa percentage) of a line width series as a function of a positionaloffset (in microns). An autocorrelation function is a measure of thesimilarity of two series. In the case which is shown in FIG. 4 a firstline width series is compared with an identical second series. The firstseries and the second series are offset from each other by differentdistances and the autocorrelation between the two series calculated ateach offset. FIG. 4 displays the calculated autocorrelation function atdifferent positional offsets between the first and second series.

A large central maximum 13 is seen around an offset of 0 μm in FIG. 4.This central maximum 13 represents a situation in which the first andsecond series are the same (since there is no offset between them) andthe series are therefore highly correlated. The height of the centralmaximum 13 is equal to the total variance (the standard deviation asquared) of the line width series. At either side of the central maximum13, a first local maximum 15 a and a second local maximum 15 b can beseen. The first and second local maxima 15 a, 15 b represent apositional offset at which there is an increased correlation between thefirst and second series (when compared to other surrounding offsets).

The power spectral density of a line width series at differentfrequencies (as shown in FIG. 3) and/or the autocorrelation of a linewidth series at different offsets (as shown in FIG. 4) may in someembodiments be used to analyse a line width series at one or morespatial frequencies. If the contribution of speckle is confined tolimited spatial frequencies then tools such as the power spectraldensity and/or the autocorrelation function may be used to separate theeffects of speckle from other stochastic effects.

There exists a Fourier relationship between the autocorrelation of thespeckle contrast in an image plane of an optical system and theintensity profile of radiation in an illumination pupil of the opticalsystem. This Fourier relationship may be used to confine thecontribution of speckle in the image plane to limited spatialfrequencies. For example, if radiation in the illumination pupil has aperiodic intensity profile then this serves to confine the contributionof speckle in the image plane to limited spatial frequencies, which aredetermined by the period of the intensity profile in the illuminationpupil.

FIG. 5 is a schematic representation of an intensity profile ofradiation in an illumination pupil of a lithographic system. Lightshades in FIG. 5 represent high intensity and dark shades represent lowintensity. The illumination pupil is a pupil plane which determines theillumination of a patterning device MA which is situated in an objectplane. The illumination pupil has a Fourier relationship with the objectplane in which a patterning device MA is situated. That is, the spatialintensity profile of radiation in the illumination pupil determines theangular intensity profile of radiation in the object plane.

The illumination system IL is operable to control the spatial intensityprofile in the illumination pupil, thereby controlling the angularintensity profile with which a patterning device MA is illuminated. Forexample, during a typical lithographic exposure, the illumination systemIL may be configured to limit the spatial extent of radiation in theillumination pupil to a plurality of pole regions (e.g. a dipole orquadrupole arrangement) so as to form a multi-pole illumination mode. Amulti-pole illumination mode causes the patterning device MA to beilluminated from one or more discrete ranges of angles.

The illumination pupil which is shown in FIG. 5 has a periodic intensityprofile in an x-direction, which is indicated in FIG. 5. In theembodiment which is shown in FIG. 5, the intensity is a sinusoidalfunction of position on the x-axis. The sinusoidal function has a periodP_(p). The sinusoidal function may, for example, be a cosine functionsuch that the radiation intensity at a central x-position in theillumination pupil (x=0 in FIG. 5) is substantially a local maximum or alocal minimum. It will be appreciated that the intensity of radiationcannot be negative at any position in the illumination pupil. Inpractice, the radiation intensity as a function of x-position in theillumination pupil may be proportional to 1+cos(x). Such an intensitydistribution is considered to be, an example, of a sinusoidal functionand an example of a cosine function.

The intensity as a function of position on the y-axis follows a Gaussiandistribution centred on a central y position y_(c) (y=0 in FIG. 5).Using a Gaussian distribution in the y-direction restricts the y-extentof the radiation in the illumination pupil to a central region of they-domain. The y-direction used herein denotes the scanning direction inwhich the substrate W and/or the patterning device MA are scannedrelative to each other. The x-direction used herein denotes thenon-scanning direction which is perpendicular to the scanning direction.

For the purposes of the methods described herein it is desirable forisofocal behaviour to occur at the substrate W. Isofocal behaviour meansthat no line width W_(L) variations are introduced due to changes infocus across the image plane. Consequently variations in the line widthW_(L) may be uniquely attributed to variations in dose and are notcaused by variations in focus. This allows the line width W_(L)variation to be measured and used to determine the dose variation.

Isofocal behaviour may be realised by restricting the extent (in theillumination pupil) of radiation in the y-direction and centring theintensity profile of radiation in the y-direction about a centraly-position y_(c). However, if the extent of the radiation in they-direction is too small then this may cause high values of localradiation intensity in the illumination system IL, which may causedamage to components of the illumination system IL. The extent of theradiation in the y-direction may therefore be about 3% or greater of they-extent of the illumination pupil.

Whilst the extent of radiation in the y-direction is restricted to acentral region of the illumination pupil, as radiation passes through apatterning device MA, one or more diffraction orders may be formed. Forexample, radiation may pass through a line feature of the patterningdevice MA and form −1, 0 and +1 diffraction orders (and may form higherorder diffraction orders). In a pupil plane of the projection system PLthe diffraction orders may be distributed in the y-direction such thatthe extent of the radiation in the y-direction is no longer restrictedto a central y-region but also includes +1 and −1 diffraction orderspositioned either side of the central y-region. In order to maintainisofocal behaviour, it may be desirable to restrict the diffractionorders which pass through the projection system PL to +1, 0 and −1diffraction orders. This may be achieved, for example, by selecting thepitch of features on the patterning device MA relative to the numericalaperture NA of the projection system PL. The pitch of the features onthe patterning device MA may, for example, be greater than λ/NA and maybe less than 2λ/NA, where λ is the wavelength of the radiation. It maybe further desirable to select the duty cycle of features on thepatterning device MA such that isofocal behaviour is maintained at lowexposure doses.

The patterning device MA may, for example, include features which have apitch of approximately 160 nm. The wavelength A of radiation may beapproximately 193 nm and the numerical aperture NA of the projectionsystem may be approximately 1.35. In such an embodiment a pitch ofapproximately 160 nm is greater than Δ/NA and less than 2λ/NA. In anembodiment each pitch may, for example, include a transmissive regionhaving a width of approximately 120 nm and an attenuating region havinga width of approximately 40 nm. This may provide a duty cycle whichmaintains isofocal behaviour at low exposure doses.

In an alternative embodiment, the patterning device MA may, for example,comprise an alternating phase shift mask which is configured to providehigher contrast than the above described patterning device. In anembodiment, the alternating phase shift mask may comprise a grating witha pitch of approximately 160 nm. The wavelength λ of radiation may beapproximately 193 nm and the numerical aperture NA of the projectionsystem may be approximately 1.35. One period of the alternating phaseshift mask may comprise a first attenuating portion with a width of 40nm, a first transparent portion with a width of 40 nm, a secondattenuating portion with a width of 40 nm and a second transparentportion with a width of 40 nm. The second transparent portion may beconfigured to apply a phase shift of 180° to incident radiation, and thefirst transparent portion may be configured to apply no phase shift.This alternating phase shift configuration acts to attenuate radiationin the zero diffraction order, and this in turn increases the contrastof the image formed on the substrate W (radiation in the firstdiffraction order is not attenuated). Attenuation of the zerodiffraction order may substantially eliminate the zero diffraction orderbecause the average E-field of the radiation in that order is zero. Inaddition to increasing the contrast of the image which is formed at thesubstrate, eliminating the zero diffraction order also advantageouslyhalves the pitch of the grating image formed at the substrate.

In a further alternative embodiment, the patterning device (NA) may, forexample comprise a grating formed as an alternating phase shift maskwhich does not include attenuating portions (i.e. the mask featurescomprise entirely of regions which apply relative phase shifts).

The intensity profile of the illumination pupil which is shown in FIG. 5is periodic in the x-direction and is used to expose line features whichextend in the x-direction. In alternative embodiments line featureswhich extend in the y-direction may be exposed. In such embodiments, theillumination pupil may be periodic in the y-direction, as opposed to thex-direction (as shown in FIG. 5). The intensity in the x-direction mayfollow a Gaussian distribution centred on a central x-position.

The intensity profile in the illumination pupil may be established bycontrolling the illumination system IL. The illumination system IL may,for example, comprise an array of mirrors whose orientation may beadjusted. Each of the mirrors of the array of mirrors may receive aportion of the radiation beam provided from the radiation source SO andmay direct the received portion of the radiation beam according to theorientation of the mirror. The orientation of mirrors may be configuredso as to form a desired spatial intensity profile in the illuminationpupil. For example, the orientation of the mirrors may be configured soas to form the spatial intensity profile which is shown in FIG. 5.

In the embodiment which is shown in FIG. 5 the illumination pupilincludes 9 periods P_(p) in the x-direction. In other embodiments theillumination pupil may include more than or fewer than 9 periods P_(p)in the x-direction. It may be desirable for the illumination pupil toinclude an integer number of periods P_(p) in the x-direction. In someembodiments, the illumination system IL may be restricted to formingsymmetric spatial intensity profiles in the illumination pupil. Forexample, the illumination system IL may form spatial intensity profileswhich exhibit reflection symmetry about a central x-position and/orreflection symmetry about a central y-position. The symmetry of theillumination pupil may restrict the possible number of periods P_(p) inthe x-direction to odd numbers of periods.

In general the spatial intensity distribution in the illumination pupilmay include a total of K periods. In some embodiments K is an integer.In some embodiments K is an odd number. The number K of periods in theillumination pupil may be greater than 2. In some embodiments the numberK of periods in the illumination pupil may be 5 or more. In someembodiments the number K of periods in the illumination pupil may 17 orless.

As was described above, providing a periodic spatial intensity profilein the illumination pupil (as shown in FIG. 5) serves to confine theeffects of speckle to limited spatial frequencies in the image plane inwhich the substrate W is situated. The spatial frequency at whichspeckle effects are visible in the image plane (in which the substrate Wis situated) has a period P_(S). The period P_(S) at which speckleeffects are visible is related to the periodicity of the spatialintensity profile in the illumination pupil according to equation (2).

$\begin{matrix}{P_{S} = \frac{\lambda \; K}{2{NA}}} & (2)\end{matrix}$

Where λ is the wavelength of the radiation beam provided by theradiation source SO, NA is the numerical aperture of the projectionsystem PL and K is the number of periods P_(p) in the illumination pupil(as was described above).

FIG. 6 is a schematic representation of an autocorrelation functionassociated with a line width series, which results from the exposure ofa lithographic line feature using a periodic illumination pupil (e.g.the illumination pupil shown in FIG. 5). As was explained above withreference to FIG. 4, the autocorrelation function includes a largecentral maximum 13 centred at a positional displacement of 0, due to ahigh correlation between identical series (with no displacement betweenthem). Either side of the central maximum 13 is situated a first localmaximum 15 a and a second local maximum 15 b. The first and second localmaxima 15 a, 15 b are situated at a distance P_(S) either side of 0 (atwhich the central maximum 13 is centred) and represent an increasedcorrelation when the line width series is offset from itself by adistance P_(S). The increased correlation displayed at the first andsecond local maxima 15 a, 15 b is caused by the effects of speckle whichhas been confined to limited spatial frequencies centred at a frequencyof 1/P_(S) by a periodic illumination pupil containing K periods. Thefirst and second local maxima 15 a, 15 b may therefore provide a measureof speckle at the substrate W. For example the height H_(L) of first andsecond local maxima 15 a, 15 b may be indicative of the contribution ofspeckle to the line width roughness.

The contribution of speckle at a spatial frequency of 1/P_(S) will alsobe visible in a representation of the power spectral density of a linewidth series as a function of frequency (not shown). The effects ofspeckle will result in a local maximum of the power spectral density atspatial frequencies of l/P_(S), where l is a positive integer and l≤K.

FIG. 7 is a representation of autocorrelation functions associated witha number of different line width series. The different line width serieswhich are shown in FIG. 7 represent the line widths which result fromexposure of line features using different illumination pupils. A firstcurve 101 which is shown in FIG. 7 represents a reference exposure inwhich an illumination pupil which is not periodic is used. A secondcurve 103 represents an exposure performed with 5 periods in theillumination pupil (K=5). A third curve 105 represents an exposureperformed with 9 periods in the illumination pupil (K=9). A fourth curve107 represents an exposure performed with 13 periods in the illuminationpupil (K=13). A fifth curve 109 represents an exposure performed with 17periods in the illumination pupil (K=17).

Each of the autocorrelation functions shown in FIG. 7 exhibit a secondlocal maximum 15 b. The autocorrelation functions also exhibit firstlocal maxima, however these are not shown in FIG. 7. As can be seen inFIG. 7, the position and height of the local maxima 15 b is differentfor different illumination pupils. As was explained above, the positionof a local maximum is the period P_(S) at which speckle effects arevisible. The period P_(S) is given by equation (2) above and depends onthe number K of periods in the illumination pupil. The position of thelocal maxima 15 b is therefore different for different numbers ofperiods K in the illumination pupil as can be seen in FIG. 7.

FIG. 8 is a representation of the position of different local maxima 15b which are observed when using different numbers K of periods in theillumination pupil. The position of the local maxima 15 b is equivalentto the period P_(S) at which speckle effects are visible. The data shownin FIG. 8 was obtained by exposing a number of different line featuresusing different numbers K of periods in the illumination pupil. The linefeatures in the substrate W were observed using a scanning electronmicroscope to produce images of the line features. The images wereanalysed to detect the edges of the line features so as determine theline widths W_(L) at different positions along the lines. Line widthsW_(L) at different positions along the lines were used to construct linewidth series.

For each illumination mode having a given number K of periods in theillumination pupil, a plurality of different line features may beexposed and a line width W_(L) series may be derived from each exposedline feature. For example, in some embodiments more than about 100 linefeatures may be exposed thereby providing more than about 100 line widthseries for a given illumination mode. In some embodiments more thanabout 1000 line features may be exposed in order to provide more thanabout 1000 line width series for a given illumination mode. A pluralityof line width series for a given illumination mode may be used tocalculate an average power spectral density for the given illuminationmode.

The average power spectral density for each illumination mode having anumber K of periods is used to calculate an autocorrelation function foreach number K of periods. The autocorrelation functions are calculatedat different positional offsets and the positions of the local maximumdetermined, thereby providing the data which is shown in FIG. 8. As canbe seen in FIG. 8, the positions of the local maxima increasesproportionally with the number of periods K as predicted by equation(2).

FIG. 9 is a representation of the height of the local maxima 15 b fordifferent values of K. As can be seen from FIG. 9, the height of thelocal maxima 15 b is different for different values of K. This variationin the height of the local maxima 15 b is largely due to differences inthe illumination modes at different values of K. Some variation in theheight of the local maxima 15 b shown in FIG. 9 may also be due to smalldifferences in experimental conditions when carrying out the exposures.

The autocorrelation function contains a contribution from speckle andcontributions from other stochastic effects (e.g. the result of chemicalprocesses which occur in a resist used during the exposure process). Aswas described above, by using a periodic illumination mode, the effectsof speckle are advantageously confined to a limited number of spatialfrequencies. Consequently the height of a local maximum 15 b in anautocorrelation function is mostly due to the contributions of speckle.The height of a local maximum 15 b thus depends at least in part on thespeckle contribution and may be used to determine the contribution ofspeckle to line width roughness. However, the height of a local maximum15 b also includes some contribution from other stochastic effects. Itis desirable to separate the contribution of speckle from othercontributions.

The contribution of speckle may be separated from other contributions byderiving a reference autocorrelation function which represents asituation in which an illumination mode which is not periodic is used(e.g. the first curve 101 which is shown in FIG. 7). For example, anillumination mode comprising an intensity profile in a pupil plane whichis not periodic may be used to expose one or more line features. Anautocorrelation function corresponding to the exposed line features maybe computed and this autocorrelation function may serve as a referenceautocorrelation function. The reference autocorrelation function willinclude contributions from speckle but these contributions are spreadacross all spatial frequencies (since a non-periodic illumination modeis used). The height of the reference autocorrelation function at eachpositional offset will therefore mostly be due to contributions otherthan speckle and which do not depend on the illumination mode which isused. The reference autocorrelation function may be subtracted from anautocorrelation function which is derived using a periodic illuminationmode in order to separate the effects of speckle from othercontributions. For example, the difference between the height of a localmaximum 15 b in an autocorrelation function derived using a periodicillumination mode and the height of the reference autocorrelationfunction at the same positional offset may be determined. The resultingdifference is a measure of the contribution of speckle to the line widthroughness (with other contributions subtracted) using a particularillumination mode.

A determined height of a local maximum 15 b in an autocorrelationfunction may be denoted H_(L). The height of a reference autocorrelationfunction at a positional offset corresponding to a local maximum 15 b inan autocorrelation function derived using a periodic illumination modemay be referred to as a reference local maximum height and may bedenoted H_(LR). The difference between the determined height H_(L) andthe reference height H_(LR) may be referred to as the speckle localmaximum height and may be denoted H_(LS) where H_(LS)=H_(L)−H_(LR).

In some embodiments a reference autocorrelation function (including thereference local maximum height H_(LR)) may be derived by means otherthan performing an exposure using a non-periodic illumination mode. Forexample, in some embodiments a reference autocorrelation function may beestimated from an autocorrelation function which is determined using aperiodic illumination mode, by considering the autocorrelation functionat positional offsets either side of a local maximum 15 b. That is, theheight of an autocorrelation function either side of a local maximum 15b may be used to estimate the height of the autocorrelation functionH_(LR) (at positional offsets corresponding to the local maximum) whichwould occur if the local maximum was not present (corresponding to acase where a non-periodic illumination mode is used).

Methods have been described above for deriving the contribution ofspeckle when using a specific illumination mode. For example, thespeckle local maximum height His provides a measure of the contributionof speckle. However, this measure is dependent on the illumination modewhich is used to form the autocorrelation function and may be differentfor different illumination modes.

It may be desirable to provide a measure of the contribution of specklewhich is independent of the illumination mode which is used during ameasurement process. This measure may then be used to estimate thecontribution of speckle when exposures are performed using illuminationmodes which are different to the illumination mode used during themeasurement process. For example, during a typical lithographic exposureprocess it may be desirable to use a multipole illumination mode (e.g. adipole illumination mode). A multipole illumination mode is different toa periodic illumination mode which may be used to measure thecontribution of speckle. It is therefore desirable to provide a measureof the contribution of speckle which is relevant to all illuminationmodes.

A measure of the contribution of speckle which is independent of theillumination mode which is used may, for example, comprise a variance(or equivalently a standard deviation σ) of line width W_(L) which iscaused by speckle. In some embodiments a measure of the contribution ofspeckle which is independent of the illumination mode which is used maycomprise a variance (or equivalently a standard deviation a) of a doseof radiation which is caused by speckle. In some embodiment a measure ofthe contribution of speckle which is independent of the illuminationmode which is used may, for example, comprise the speckle contrast C.Equivalently a measure of the contribution of speckle which isindependent of the illumination mode which is used may comprise thenumber N of independent speckle patterns to which a given point on asubstrate is exposed during a single exposure period. As was explainedabove, in embodiments in which the radiation source SO comprises a laser(e.g. an excimer laser) the number N of independent speckle patterns isequal to the number of active independent laser modes which are excitedin the laser during an exposure period.

As was mentioned above the height of the central maximum 13 of anautocorrelation function is equal to the total variance (standarddeviation σ squared) of a line width series. It may be desirable todetermine the variance (or equivalently the standard deviation σ) of aline width series which is due to speckle. That is, it may be desirableto determine the height of the central maximum (i.e. the total variance)which would result if the only contributor to the variance was speckle.Using the measurement process described above the height of a resultingcentral maximum 13 (i.e. the total variance) will include othercontributions as well as the contributions from speckle. A determinationof the height of the resulting central maximum 13 using the abovedescribed measurement process does not therefore directly lead to thecontribution of speckle to the variance.

In some embodiments the height of a local maximum 15 b may be used toestimate the height of a central maximum 13 in an autocorrelationfunction corresponding to variation which is only caused by speckle.That is, the height of a local maximum 15 b may be used to estimate thetotal variance due to speckle. An autocorrelation function correspondingto variation only caused by speckle may be referred to as the speckleautocorrelation function. As was explained above, after subtraction of areference autocorrelation function, the height of a local maximum 15 bin an autocorrelation function (referred to as the speckle local maximumheight His) may be considered to be only due to the effects of speckleand not due to any other contributions. The speckle local maximum heightHis may therefore be considered to be a point on a speckleautocorrelation function. If the general shape of the speckleautocorrelation function is known then the determination of a point onthe speckle autocorrelation function may be used to determine otherpoints on the speckle autocorrelation function. In particular if theratio between a local maximum 15 b and a central maximum 13 in a speckleautocorrelation function is known then the determination of the ofspeckle local maximum height His may be used to determine the height ofa central maximum in the speckle autocorrelation function.

The height of the central maximum 13 in a speckle autocorrelationfunction may be referred to as the speckle central maximum height andmay be denoted H_(CS). As was explained above it may be desirable todetermine the ratio R_(S) between the speckle central maximum heightH_(CS) and the speckle local maximum height H_(LS) as given by equation(3).

$\begin{matrix}{R_{S} = \frac{H_{LS}}{H_{CS}}} & (3)\end{matrix}$

The ratio R_(S) may be used to determine the speckle central maximumheight H_(CS) from an experimentally determined value of the specklelocal maximum height H_(LS). The ratio R_(S) may depend on theillumination mode which is used. It may therefore be desirable todetermine the ratio R_(S) for the same illumination mode for which thedetermination of the speckle local maximum height His is performed.

In some embodiments, the ratio R_(S) may be determined throughmeasurement of the intensity profile of the illumination pupil. Theintensity profile of the illumination pupil may, for example, bedetermined by measuring the angular intensity profile of radiation whichis received at an image plane of the projection system PL. For example,a patterning device MA comprising a small pin-hole aperture may bepositioned in an object plane such that radiation only passes through asmall extent of the object plane. The aperture in the patterning deviceMA receives radiation having an angular distribution which depends onthe illumination pupil being used. Radiation propagates through theaperture and through the projection system PL and is imaged onto animage plane (a plane in which a substrate W is located during alithographic exposure). The angular intensity profile of radiation inthe image plane may be measured using one or more image sensors. Forexample a wavefront sensor may be used to derive the angular intensityprofile of radiation in the image plane. A wavefront sensor which may beused to derive the angular intensity profile of radiation in the imageplane may already be present in a lithographic apparatus and may beoperable to measure wavefront aberrations caused by the projectionsystem PL.

The angular intensity profile in the image plane is equivalent to thespatial intensity profile in the illumination pupil. A Fourier transformof the spatial intensity profile in the illumination pupil (orequivalently the angular intensity distribution in the image plane) maybe determined. The Fourier transform, of the spatial intensity profileof the illumination pupil is equivalent to the autocorrelation functionof the intensity profile in a field or image plane (e.g. the image planein which a substrate W is situated). The Fourier transform of thespatial intensity profile of the illumination pupil may therefore bereferred to as the autocorrelation function of the illumination pupil.

FIG. 10 is a representation of the autocorrelation function of ameasured intensity in an illumination pupil at different positionaloffsets. The autocorrelation function which is shown in FIG. 10 iscalculated by measuring the intensity in the illumination pupil atdifferent positions. At each x-position the radiation intensity over ally-positions may be summed to provide a sum of the radiation intensity ata given x-position. Summations over y of the radiation intensity atdifferent x-positions provides a series of intensity measurements atdifferent x-positions. A Fourier transform of this series may beperformed in order to determine the autocorrelation function which isshown in FIG. 10. The autocorrelation function which is shown in FIG. 10is shown as a percentage of the height of a central maximum (not shownin FIG. 10) in the autocorrelation function.

As can be seen in FIG. 10 a local maximum 15 b occurs in theautocorrelation function. The local maximum 15 b lies at a positionwhich is equivalent to the period P_(p) of the periodic intensityprofile in the illumination pupil and has a height which isapproximately 25% of the height of a central maximum in theautocorrelation function.

The ratio between the central maximum height and the local maximumheight may be approximately the same for the autocorrelation function ofthe intensity profile of the illumination pupil as it is for the speckleautocorrelation function. The ratio between the central maximum heightand the local maximum height may therefore be determined from theautocorrelation function of the intensity profile of the illuminationpupil and may be used as an estimate of the ratio R_(S) which is givenby equation (3). The estimated ratio R_(S) may be used to determine thespeckle central maximum height H_(CS) from the speckle local maximumheight His by rearranging equation (3).

FIG. 11 is a representation of the height of the local maximum 15 b inthe autocorrelation function of the of the illumination pupil (as apercentage of the height of the central maximum in the autocorrelationfunction) for different illumination modes having different values ofthe number of periods K in the illumination pupil. The heights of thelocal maxima as shown in FIG. 11 and as expressed as a percentage mayprovide an estimate of the ratio R_(S) (as expressed by equation (3))for a number of different numbers of periods K in the illumination pupil

Using the above described process it is possible to deduce thecontribution of speckle to the variance of line width roughness. Forexample, in a particular experiment an illumination mode having 17periods in the illumination pupil (i.e. K=17) was used to expose anumber of line features. Measurements of the resulting line width atdifferent positions along the exposed line features were used todetermine an autocorrelation function similar to the autocorrelationfunction which is shown in FIG. 6. It was deduced that the height of acentral maximum 13 in the autocorrelation function associated with ameasured line width series was approximately 3.68 nm². As was describedabove, the height of the central maximum 13 in the autocorrelationfunction is equal to the total variance (including contributions fromspeckle and other effects) in the line width. The corresponding standarddeviation a (the square root of the variance) is approximately 1.92 nm.

As can be seen from FIG. 7 the height of the local maximum in theautocorrelation function associated with a value of K=17 was found to beapproximately equal to 0.12 nm². FIG. 11 shows that at a value of K=17,the height of a local maximum of the autocorrelation function associatedwith the illumination pupil is approximately 20%. The ratio R_(S)between the speckle central maximum height H_(CS) and the speckle localmaximum height H_(LS) for a value of K=17 is therefore approximately0.2. By rearranging equation (3) the speckle central maximum heightH_(CS) is given by H_(L)s/R_(S)=0.12/0.2=0.6 nm². As was explainedabove, the speckle local maximum height His is the variance in the linewidth which is caused by speckle. The variance which is caused byspeckle is therefore estimated to be 0.6 nm². The corresponding standarddeviation a of the line width which is caused by speckle is given by√{square root over (0.6)}=0.77 nm.

The variation in the line width which is caused by speckle may be usedto determine the variation in dose which is caused by speckle. As wasexplained above the line width of a feature depends on the dose ofradiation which is received. The variation in line width of a featuretherefore depends on the variation in the dose of radiation which isreceived. The relationship between the dose of radiation and the linewidth is dependent on the illumination pupil which is used and may bedetermined by separate experimentation. For example, experiments may beperformed in which a number of different line features are exposed usinga given illumination mode. The dose of radiation to which the substrateis exposed may be varied and the resulting variation in the line widthmay be measured. These measurements may be used to derive thesensitivity of the line width to variations in the dose for a particularillumination mode. The same process may be performed using a number ofdifferent illumination modes in order to derive the sensitivity of theline width to variations in the dose for each illumination mode.

The sensitivity of the line width to variations in the dose for a givenillumination mode may be used to convert a line width variation into adose variation. For example, a lookup table of sensitivities of the linewidth to variations in dose for different illumination modes may bestored. The lookup table may be referred to and may be used to convert ameasured line width variation into a dose variation. The linewidthvariation which is caused by speckle may depend on the illumination modewhich is used. However, the dose variation which is caused by specklemay be independent of the illumination mode which is used. The dosevariation which is caused by speckle may therefore be a useful measureof speckle which provides information about the contribution of speckleusing any illumination mode.

Using the method described above, in a particular experiment it wasdetermined that a standard deviation a of 0.77 nm in the line widthwhich is caused by speckle corresponds to a dose variation along a linefeature of approximately 0.64% due to speckle. As was explained abovethis dose variation is independent of the illumination mode.

A method has been described above in which the ratio R_(S) between thespeckle central maximum height H_(CS) and the speckle local maximumheight His is estimated from a measurement of the spatial intensityprofile of the illumination pupil. In other embodiments the ratio R_(S)may be estimated using other means. For example, in some embodiments asimulation may be used to estimate the ratio R_(S). For example, asimulation of radiation propagating through the projection system PL maybe performed in order to derive a simulated speckle pattern. Anautocorrelation function may be derived from the simulated specklepattern. The height of the central maximum and the height of a localmaximum in the simulated autocorrelation function may be used todetermine the ratio R_(S) of the height of the local maximum to theheight of the central maximum. The ratio R_(S) which is derived throughsimulation may be used to determine a speckle central maximum heightH_(CS) from a speckle local maximum height H_(LS) which is determinedthrough experimentation.

One example of a simulation which may be used to determine a simulatedspeckle pattern may be a Monte Carlo simulation. For example, a coherentMonte Carlo simulation may be used to simulate the propagation ofradiation through a lithographic apparatus. The input to the simulationmay comprise a plurality of radiation sources situation in a plane. Eachradiation source may have the same intensity and the relative phase ofeach source may be simulated as being random. The effect of theillumination system IL, the patterning device MA and projection systemPL may be simulated by amplitude filters. At each position in an imageplane of the projection system the intensity from each radiation sourcemay be summed to define an intensity at that position. The output of thesimulation may therefore be an intensity distribution of radiation inthe image plane. The output intensity distribution may be used to derivean autocorrelation function from which the ratio R_(S) may be derived.

In some embodiments a classical simulation of partially coherentradiation sources may be performed. The simulation may be used to outputan optical transfer function of the lithographic apparatus. The opticaltransfer function is equivalent to the power spectral density from whichan autocorrelation function may be derived. The autocorrelation functionmay be used to determine the ratio R_(S).

A simulation of partially coherent radiation sources may comprise,modelling the intensity distribution in the illumination pupil as aseries of incoherent point radiation sources. Simulated point sourcesmay, for example, be arranged so as to emulate a periodic illuminationmode as was described above (for example, the periodic illumination modedepicted in FIG. 5). The envelope of the distribution of point sourcesin the illumination pupil matches the illumination pupil filling. Thepropagation of radiation from each point source through the patterningdevice MA and the projection system is simulated so as to provide asimulation of radiation incident in an image plane of the projectionsystem at which a substrate W is situated. The patterning device MA maybe simulated as a periodic series of transmissive lines (e.g. linesextending in a non-scanning direction). For example, the patterningdevice MA may be simulated as a periodic line pattern having a period ofapproximately 160 nm.

At the patterning device MA, radiation from each point source in theillumination pupil translates into a plane wave propagating in a givendirection. The patterning device MA serves to diffract the simulatedplane wave into multiple beams. In the projection system PL, thediffraction pattern may be truncated by the limited numerical apertureNA of the projection system PL. In an image plane of the projectionsystem the intensity profile which results from each point source in theillumination pupil is determined. A summation of the intensity profilesin the image plane resulting from each point source is then performed soas to derive the total intensity profile in the image plane. Thesummation of the contributions from each point source is performed as anincoherent sum. The simulation of the propagation of radiation throughthe lithographic apparatus is performed as a coherent sum (i.e. asummation of amplitudes).

In some embodiments, other factors may be taken into account in asimulation. For example, the propagation of radiation into a resistsituated in the image plane and/or subsequent development of the resistmay be simulated. In some embodiments, the effects of polarization ofthe radiation may be accounted for in the simulation. For example,polarization effects in the illumination pupil, at the patterning deviceMA, and in the image plane may be accounted for in the simulation. Insome embodiments, a simulation may additionally account forthree-dimensional imaging effects, for example, at the patterning deviceMA and at the substrate W.

Examples of simulations of partially coherent radiation sources whichmay be used in embodiments of the invention may, for example, includeHyperlith, Prolith and/or Solid-C simulations.

In some embodiments, simulations may be performed using differentconfigurations of the simulated patterning device MA. For example, oneor more properties of a simulated patterning device MA may be modulatedand a resulting modulation in an output of the simulation (e.g. asimulated radiation intensity profile in an image plane) may bedetected. The amplitude of a detected modulation in an output of thesimulation may allow a transfer function of the modulation to bedetermined. A modulation transfer function may be derived as a functionof frequency. As was explained above, an optical transfer function of anoptical system (e.g. a modulation transfer function) is equivalent to apower spectral density from which an autocorrelation function may bederived. The autocorrelation function may be used to determine the ratioR_(S).

In some embodiments one or more properties of a simulated patterningdevice MA may be modulated with a modulation amplitude of approximately5% or less of a mean value of the property. In some embodiments, a widthof a simulated patterning device MA may be modulated as described above.

In some embodiments the ratio R_(S) may be determined experimentally.For example, a plurality of exposures may be performed using differentnumbers of pulses of the radiation source SO in a single exposureperiod. As was explained above, the number of pulses to which a point ona substrate is exposed affects the number N of independent specklepatterns to which the point is exposed during a given exposure period(assuming that the duration of the pulse remains the same). For exampleincreasing the number of pulses during an exposure period will increasethe number N of speckle patterns to which a point on the substrate isexposed.

FIG. 12 is a schematic representation of an intensity profile ofradiation in an illumination pupil of a lithographic system according toan alternative embodiment of the invention. Lighter areas in FIG. 12represent higher intensity of radiation and darker areas represent lowerintensity of radiation. The radiation is in a dipole mode, i.e. with noradiation in the centre of the illumination pupil in the y-direction butwith radiation poles separated in the y-direction (at y-direction edgesof the illumination pupil). The illumination pupil schematicallydepicted in FIG. 12 has a periodic intensity profile in the x-direction.The intensity profile may be a sinusoidal function of position in thex-direction.

For each pole of the dipole, the intensity as a function of position iny-direction may follow a Gaussian distribution. The intensitydistribution of the poles of the dipole may be configured to provideisofocal behaviour in the manner discussed further above in connectionwith FIG. 5.

An advantage arising from using a dipole illumination mode instead of acentrally positioned illumination mode of the type depicted in FIG. 5,is that the dipole illumination mode will provide higher contrast of theimage formed on the substrate (V). A dipole illumination mode of thetype depicted in FIG. 12 may for example be used in connection with apatterning device provided with a grating extending in the y-direction.An example of a repeating unit of such a grating is schematicallydepicted in FIG. 13. The grating may have a pitch of approximately 80nm. Each unit of the grating may for example have an opaque portion witha width of approximately 40 nm and a transmissive portion with a widthof approximately 40 nm. This grating may be used in combination with awavelength λ of radiation of approximately 193 nm and a projectionsystem with a numerical aperture NA of approximately 1.35.

The patterning device may comprise a conventional (binary) mask (asdepicted), an alternating phase shift mask or an attenuating phase shiftmask (e.g. with attenuation of around 6%).

In general, the patterning device of any of the embodiments of theinvention may comprise a conventional (binary) mask, an alternatingphase shift mask or an attenuating phase shift mask (e.g. a 6%attenuating phase shift mask).

In general, the contribution of speckle to a central maximum 13 in anautocorrelation function is approximately inversely proportional to thenumber N of independent speckle patterns. That is, the contribution ofspeckle to the central maximum scales with 1/N. The contribution ofnon-speckle effects to the central maximum is not substantially affectedby changes in the number N of independent speckle patterns. The gradientwith which the height of the central maximum 13 changes with changes in1/N is therefore independent of the contribution of non-speckle effectsto the central maximum height. Non-speckle effects instead introduce anoffset to the height of the central maximum 13 which is independent of1/N.

A plurality of exposures may be performed using different numbers ofpulses in a given exposure period. As was explained above, changing thenumbers of pulses in an exposure period will change the number N ofindependent speckle patterns to which each point on the substrate isexposed. For each number of pulses in the exposure period anautocorrelation function may be derived and the height of a centralmaximum 13 in the autocorrelation function may be determined. Using thismethod, changes in the height of the central maximum 13 may be observedat different values of the number N of independent speckle patterns. Thegradient with which the height of the central maximum 13 changes withchanges in 1/N may be determined from these measurements along with theoffset in the height of the central maximum 13 which is caused bynon-speckle effects. This allows the contribution of speckle to theheight of the central maximum to be separated from the contribution ofnon-speckle effects to the central maximum. Consequently the specklecentral maximum height H_(CS) (and therefore the variance due tospeckle) may be determined for each exposure. This method also allowsthe ratio R_(S) to be determined by also determining the height of alocal maximum in the autocorrelation function which results from eachexposure.

Methods have been described above in which the line width and/or dosevariance which is caused by speckle. The above described measurementsand methods may additionally or alternatively be used to determine thenumber N of independent speckle patterns to which a given point on asubstrate is exposed during an exposure period. As was explained above adetermination of the ration R_(S) allows a standard deviation a which iscaused by speckle to be derived. The number N of independent specklepatterns to which a given point on a substrate is exposed may be derivedfrom the standard deviation a by rearranging equation (1) to giveequation (4) below.

$\begin{matrix}{N = ( \frac{\overset{\_}{I}}{\sigma} )^{2}} & (4)\end{matrix}$

As was described above a parameter which is indicative of thecontribution of speckle may be obtained from one or more exposuresperformed using a single illumination mode. The parameter which isdetermined using a single illumination mode may be independent of theillumination mode which is used. For example, a dose variation which iscaused by speckle may be determined using a single illumination mode.The dose variation may be independent of the illumination mode which isused to determine the dose variation. Additionally or alternatively thenumber N of independent speckle patterns to which a given point on asubstrate is exposed may be determined. In some embodiments only asingle illumination mode with a single number K of periods in theillumination pupil may be used in order to determine the contribution ofspeckle. This measure may then be applicable to all illumination modes.

In general any number K of periods in the illumination pupil may beselected in order to perform a measurement process to determine thecontribution of speckle. It can be seen from equation (2) thatincreasing the number K of periods in the illumination pupil will leadto an increase in the period P_(S) in the image plane at which thespeckle has an effect. In order to determine the contribution of speckleit may be desirable to measure the line width W_(L) over a given numberof speckle periods P_(S) in the image plane. Increasing the speckleperiod P_(S) will lead to an increase in the length along a linefeature, which a given number of speckle periods P_(S) occupies.Increasing the speckle period P_(S) may therefore lead to an increase inthe length of the line width W_(L) series which is measured in order todetermine the contribution of speckle.

As was described above, in some embodiments a line width series may bedetermined by taking an image of an exposed line feature using ascanning electron microscope. A scanning electron microscope may have alimited field of view. If the length of a line width W_(L) series isgreater than the field of view of a scanning electron microscope thenmultiple images may be taken along the length of the line feature andthe images may be stitched together in order to determine the full linewidth W_(L) series. Stitching together of images may introduce an errorinto the determination of the line width W_(L) series and may thereforereduce the accuracy with which the line width W_(L) series isdetermined. In some embodiments it may be desirable to use anillumination mode which has a sufficiently small number K of periodsthat a given number of speckle periods P_(S) on the substrate W fit intoa single field of view of a scanning electron microscope. This may avoidthe need to stitch several scanning electron microscope images togetherin order to determine a full line width W_(L) series.

Determining the contribution of speckle to a variation in a lithographicprocess (e.g. a dose variation or line width variation) as was describedabove may advantageously allow a lithographic process to be optimisedwhilst accounting for the contribution of speckle. For example, withknowledge of the contribution of speckle, other aspects of alithographic process may be designed in order to account forcontribution of speckle. In some embodiments post-processing steps maybe used in order to reduce line width roughness after a substrate isexposed and developed.

In some embodiments if the contribution of speckle is found to be toohigh (for example it is determined that the contribution of speckleexceeds a threshold), then actions may be taken in order to reduce thecontribution of speckle. For example, one or more properties of theradiation source SO may be changed in order to increase the number N ofindependent speckle patterns which occur during an exposure period. Oneway in which the number N of independent speckle patterns may beincreased is to increase the number of laser pulses which occur during asingle exposure period. Increasing the number of laser pulses whichoccur during a single exposure period may, however, decrease thethroughput of a lithographic apparatus (the number of substrates whichare exposed per unit of time).

Additionally and/or alternatively the pulse duration of pulses of theradiation beam emitted from the radiation source SO may be increased.For example, one or more pulse stretchers configured to increase theduration of a pulse of radiation may added to the optical path of theradiation beam (e.g. between the radiation source SO and theillumination system IL).

Additionally or alternatively the number N of independent specklepatterns which are seen during an exposure period may be increased byincreasing the bandwidth of radiation which is emitted from theradiation source SO. In embodiments in which the radiation source SOcomprises a laser, increasing the bandwidth of radiation which isemitted from the radiation source SO will increase the number of activeindependent laser modes and therefore the number of independent specklepatterns.

Apparatus and methods have been described above which allow thecontribution of speckle to a variation in a lithographic feature to bedetermined. Such a determination may be advantageously used to monitor achange in the speckle contribution which results from a change in aproperty of a lithographic process. For example, one or more propertiesof the radiation beam which is emitted from the radiation source SO maybe altered and the resulting change in the speckle contributionmeasured. For example, the bandwidth of the radiation beam which isemitted from the radiation source SO and the corresponding change in thespeckle contribution may be measured.

It has been shown through experimentation that decreasing the bandwidthof the radiation beam which is emitted from the radiation source SOcauses an increase in the speckle contribution to line width roughness.Determining the change in speckle which is caused by a change inbandwidth advantageously allows the benefits of changing the bandwidthto be assessed and allows a suitable bandwidth to be selected whichproduces a desired results.

FIG. 14 is a photograph showing lines of a grating which have beenimaged onto a substrate using a lithographic apparatus. The radiationhad a wavelength of 193 nm and was x-polarized. The mask was analternating phase shift mask provided with a grating having a pitch ofapproximately 160 nm. The numerical aperture of the lithographicapparatus was 1.35. The illumination mode was a single on axis pole withan x-direction modulation of 700 nm with 7 periods (K=7). The photographwas generated using a scanning electron microscope. As may be seen, thegrating extends in the y-direction (i.e. it is periodic in they-direction), with individual lines of the grating extending in thex-direction. As has been explained above, the width W_(L) of each linemay be measured as a function of x-direction position. The resultingwidth data for each line may then be correlated with itself (i.e. thewidth of each line is correlated with itself along the x-directionlength). This provides an autocorrelation function which can be used todetermine how much line width variation (equivalent to criticaldimension variation) is caused by speckle. As is explained above, usingthe autocorrelation function to obtain a generally applicable measure ofthe contribution of speckle (i.e. independent of illumination mode) mayinclude measuring the intensity profile of the illumination pupil orgenerating a simulation of this. The following is a description of analternative method which may be simpler and easier to implement thanpreviously described methods.

Instead of performing a one dimensional autocorrelation along each linein the x-direction, a two dimensional correlation is performed.Referring to FIG. 14, the autocorrelation of the width W_(L) of eachline along the x-direction is performed. The x-direction correlation ofthe width W_(L) of each line relative to the next adjacent line isperformed. The x-direction correlation of the width W_(L) of each linerelative to the line which is not adjacent but is the next line afterthe adjacent line is performed (i.e. lines which are separated by anintermediate line are correlated). The x-direction correlation of thewidth W_(L) of each line relative to lines which are separated by twointermediate lines is performed. Further x-direction correlations ofline widths W_(L) for greater separations between lines are alsoperformed.

As has been explained further above, the width of imaged lines varies asa function of x-direction position, with part of the width variationbeing caused by speckle. The width variation is caused by variation ofthe intensity of radiation which forms the lines, part of this intensityvariation being caused by speckle. The standard deviation σ of the linewidth (which may be referred to as critical dimension standarddeviation) therefore depends in part on speckle.

It has been found that the y-direction position of lines also includessome variation which includes a contribution caused by speckle. They-direction position of the lines is affected by the gradient ofintensity change at edges of the lines (i.e. the rate at which theintensity changes from high intensity to low intensity). The gradient ofintensity changes is affected by speckle. Consequently, the standarddeviation σ of the line position dY depends in part upon speckle.

FIG. 15 is a graph generated using a simulation. The simulation used thesame parameters as the experimental setup used to generate the image inFIG. 14. That is, x-polarized radiation with a wavelength of 193 nm,alternating phase shift mask with a grating having a pitch of 160 nm,and lithographic apparatus numerical aperture of 1.35. A single on axispole with an x-direction modulation of 700 nm with 7 periods (K=7) wasused. The simulation was a Monte Carlo simulation using a radiationE-field having an amplitude of 1 and random phase (distributed between−180 degrees and +180 degrees), run many hundreds of thousands of times,using a simulated lithographic apparatus projection system.

As may be seen from FIG. 15, the standard deviation σ of the criticaldimension CD of lines varies linearly as a function of 1/sqrt(N). Asnoted further above, a measure of the contribution of speckle which isindependent of the illumination mode which is used comprises the numberN of independent speckle patterns to which a given point on a substrateis exposed during a single exposure period. When the source SO is alaser, the number of independent speckle patterns N is equal to thenumber of active independent laser modes which are excited in the laserduring an exposure period. Thus, the linear variation of line criticaldimension standard deviation as a function of 1/sqrt(N) confirms therelationship between the line critical dimension and speckle.

As may also be seen from FIG. 15, the standard deviation σ of they-direction position dY of the lines also varies linearly as a functionof 1/sqrt(N). Thus, the y-direction position dY of lines has the samedependency upon speckle as the line critical dimension. Although theeffect of speckle upon the y-direction position dY is less strong thanthe effect of speckle upon the critical dimension CD, because it islinear with respect to 1/sqrt(N) it can nevertheless be used to assistin speckle determination. The effect is smaller for line positionvariation dY than it is for CD variation because the gradient ofintensity change is relatively small compared with intensity variation.

FIG. 16 depicts a two dimensional correlation function generated usingthe simulation. The correlation function is expressed in nm² as afunction of positional offset along the lines (in microns). As may beseen, the correlation function includes a central maximum and first andsecond local maxima which are spaced apart from the central maximum. Ashas been explained further above, the first and second local maxima arecaused by speckle in combination with the periodic modulation of theillumination mode. Along the y-direction, which corresponds withy-direction separation of lines, these maxima decay as the y-directionseparation increases. The zero position of dY corresponds withcorrelation of each line with itself, and as would be expected providesthe highest maxima. Either side of the zero position the correlationfunction is a correlation of the line width of each line with respect toadjacent lines. Either side of this the correlation function is acombination of the line width of each line with respect to secondadjacent lines (i.e. lines separated by an intermediate line), and soon. As the separation (in terms of numbers of lines) between correlatedlines increases, the maxima of the two dimensional correlation functionreduce in height.

FIG. 17 depicts experimental results obtained using the photographdepicted in FIG. 14. The results are shown for the correlation of eachline with itself, the correlation of each line with adjacent lines, thecorrelation of each line with second adjacent lines, etc. As may beseen, the top of the central maximum of the autocorrelation function isnot visible when each line is correlated with itself. However, the topof the central maximum of the autocorrelation function is visible whenadjacent lines are correlated. Similarly, the top of the central maximumis visible when second adjacent lines are correlated. As the separationbetween correlated lines increases the height of the central maximumreduces. In other words, the greater the separation between lines whichare correlated with each other, the smaller the autocorrelation functionmaxima become.

The data depicted in FIG. 17 can be used to determine the effect ofspeckle. First, a background level is determined by looking at dataobtained with lines that are widely separated from each other (e.g.separated by 7 intermediate lines or more), and this is subtracted fromthe data obtained for other lines. Then, the ratio R_(S) between theheight of the local maxima His and the height of the central maximumH_(CS) is determined for different line separations. The average of thisratio is then determined. The average ratio R_(S) is then used, incombination with the speckle local maximum height His for lines whichare correlated with themselves, to estimate the height of the centralmaximum H_(CS) caused by speckle for lines which are correlated withthemselves. This determines the CD variance of the lines of the imagewhich is caused by speckle (in other words the speckle contribution tothe central maximum).

The CD variance due to speckle (as measured in nm²) may be converted todose variation and thereby used to determine the number of independentspeckle patterns N of the radiation source. This may be done by usingexperimental data which links the variation of feature size (e.g. linewidth) to the dose of radiation delivered to the substrate. Theexperimental data may be generated using a so called focus exposurematrix, in which a grating is exposed on a substrate using differentdoses of radiation and using different positions relative to the focalplane, and the widths of lines of the imaged grating are measured. Therelationship between line width and dose is applied to the CD variancecaused by speckle to convert it to dose variance caused by speckle(which may equivalently be referred to as intensity variance). This canthen be converted using equation (1) to a measurement of the number ofindependent speckle patterns N of the radiation source (the number ofindependent laser modes if the source is a laser). Although anembodiment which uses particular parameters such as specific maskgrating dimensions has been described, it will be appreciated that otherembodiments may be used. In general, a pattern comprising a gratingwhich will form an image of lines on a substrate may be used. Thepattern may be used in combination with a modulated illumination mode.The width variation of lines as correlated with themselves and ascorrelated with other lines may be analysed to determine speckle.

In an embodiment, the positional variation of the lines dY may be usedto determine speckle. This may be done by correlating the positionalvariation of the lines dY for each line, each adjacent line, linesseparated from each other by an intermediate line, etc. The results ofthis two-dimensional correlation may then be used, in combination with asimulation of the effect of speckle on line position variation, todetermine speckle (in a manner analogous to that described above forother embodiments).

FIG. 18 schematically depicts an illumination mode which may be used bya further alternative embodiment of the invention. The illumination modeis a quadrupole mode, with poles at x-direction edges and y-directionedges of the illumination pupil. Unlike illumination modes of previouslydepicted embodiments, each pole of the illumination mode of FIG. 18 doesnot include a modulation. However, the illumination mode as a wholeeffectively includes some modulation due to the spatial separationbetween opposite poles of the mode.

FIG. 19 depicts schematically one repeating unit of a pattern providedon a patterning device which may be used in combination with theillumination mode of FIG. 18 to enable measurement of speckle. Thepattern comprises a two dimensional grid of squares. The squares may forexample be opaque (e.g. formed from chromium) with transparent areasbeing provided between the squares. In one example, as depicted, eachsquare may measure 40 μm×40 μm, and each square may be separated fromadjacent squares in the x and y directions by a gap of 40 μm. Thus, arepeating unit which measures 80 μm×80 μm is provided (as depicted). Theillumination mode and the pattern may for example be used for aradiation source with a wavelength of 193 nm and a projection systemwith a numerical aperture of 1.35. In other embodiments the pattern maycomprise a two dimensional grid with other dimensions. The pattern maybe formed using a binary (conventional) mask, a phase shift mask, or anattenuating phase shift mask.

The pattern on the patterning device generates a grid (or twodimensional array) of features on the substrate. The features may bereferred to as holes. The holes may be photographed using a scanningelectron microscope and properties of the holes may then be analysed.

The quadrupole illumination mode generates a diffraction pattern whichis in the form of a two dimensional array of features. The orientationand pitch of the features of the two dimensional array is determined bythe quadrupole illumination mode. The orientation may be selected tocorrespond with the x and y directions by separating the poles in the xand y directions (as depicted). The pitch of the features is determinedby Braggs' law, and depends upon the wavelength of the radiation and thedistance between opposite poles. In this embodiment the wavelength is193 nm and the separation between the poles is 193/80=2.41. Thus thefeatures are optimally imaged with a relative pole position of:193/(80×2×1.35)=0.89 (from a central point of the pupil) and a relativepole separation from each other of 1.78.

The image formed on the substrate is a combination of a patterngenerated by the mask pattern and diffraction features generated by thequadrupole illumination mode. Variation of the size of the imaged holes,which corresponds with critical dimension variation, may be measured.Variation of the relative positions in the x-direction (dX) and they-direction (dY) of the imaged holes may also be measured. The resultsof these measurements may be used to determine the effect of speckle.This is because speckle shows up as a correlation between properties ofneighbouring holes.

FIG. 20 shows the results of a simulation in which a patterning deviceprovided with a grid of squares as depicted in FIG. 19 was illuminatedusing a quadrupole mode as depicted in FIG. 18. The wavelength ofradiation was 193 nm, TE polarised and the numerical aperture of thelithographic apparatus was 1.35. The simulation was a Monte-Carlosimulation using a radiation E-field having an amplitude of 1 and randomphase (distributed between −180 degrees and +180 degrees), run manyhundreds of thousands of times

As may be seen from FIG. 20, the standard deviation σ of the criticaldimension CD of holes varies linearly as a function of 1/sqrt(N). Thislinear variation as a function of 1/sqrt(N) confirms the relationshipbetween the hole critical dimension and speckle.

As may also be seen from FIG. 20, the standard deviation σ of thex-direction position dX of the holes varies linearly as a function of1/sqrt(N). Thus, the x-direction position dX of holes has samedependency upon speckle as the line critical dimension, i.e. it islinear as a function of 1/sqrt(N). The effect of speckle upon thex-direction position dX is very similar in magnitude to the effect uponthe critical dimension CD. From a comparison with FIG. 15 it may be seenthat the variation of the standard deviation of hole position as afunction of 1/sqrt(N) is significantly greater than the positionvariation seen with grating lines. This is because the gradient ofintensity change for features of the grid is steeper than the gradientof intensity change for the grating lines.

As may also be seen from FIG. 20, the standard deviation σ of they-direction position dY of the holes also varies linearly as a functionof 1/sqrt(N). The effect of speckle upon the y-direction position dY isvery similar in magnitude to the effect upon the critical dimension CDand the effect upon the x-direction position dX.

The total variance of the critical dimension of holes is affected byspeckle and by various other factors. However, correlation between thecritical dimensions of neighbouring holes is only affected by speckleand is not affected by other properties of the radiation. Similarly,x-direction position variation and y-direction position variationbetween neighbouring holes is only affected by speckle and is notaffected by other properties of the radiation.

Using the results of the simulation, the two dimensional autocorrelation of the critical dimension of the holes may be determined. Inother words, an autocorrelation of hole size is determined for the gridof holes, to obtain an autocorrelation function. A correlation of holesize for the grid of holes with respect to immediately adjacent holes inthe x-direction is also determined. A correlation of hole size for thegrid of holes with respect to holes separated in the x-direction by anintermediate hole is determined. A correlation of hole size for the gridof holes with respect to holes separated in the x-direction by twointermediate holes is determined, etc. Corresponding correlations aredetermined in the y-direction. Correlations are also performed forcombinations of x-direction and y-direction separations between holes.

FIG. 21 depicts the results of the simulation referred to above. The twodimensional correlation of hole size in a simulated image was generatedas a function of x-direction and y-direction separation by determiningthe size of all of the holes in the x and y directions and thencorrelating these as a function of hole separation from each other.

In FIG. 21, the central maximum is a correlation of the size of eachhole with itself (an autocorrelation). The size of this maximumindicates the total variance of critical dimension caused by speckle(other causes of critical dimension variation which are seen in practicewhen images are actually formed using a lithographic apparatus notpresent in the simulation). Either side of the central maximum, thecorrelation of critical dimension for neighbouring holes is alsodetermined solely by speckle. The relative size of the criticaldimension variance at the central maximum and the critical dimensionvariance either size of the central maximum is determined using the datagenerated by the simulation.

A lithographic apparatus is used to project the mask pattern of FIG. 19onto a substrate using radiation with the illumination mode depicted inFIG. 18. The radiation has properties as described above for thesimulation: wavelength 193 nm, etc. A two dimensional correlation ofhole size in the resulting image is generated as a function ofx-direction and y-direction position by determining the size of all ofthe holes in the x and y directions and then correlating these as afunction of hole position relative to each other. The central maximumobtained using the two dimensional correlation indicates the totalvariance of critical dimension, including variance caused by speckle andvariance due to other causes. Either side of the central maximum, thecritical dimension variance for neighbouring holes is determined solelyby speckle (or almost exclusively by speckle). This is because theseparation between holes is sufficiently large that other effects, whichhave short correlation lengths, do not extend to adjacent holes (or theeffects are very small at adjacent holes).

Using the simulation, the relative size (ratio) of the criticaldimension variance at the central maximum and the critical dimensionvariance either size of the central maximum has been determined. Thesize of the critical dimension variance either side of central maximumin an image exposed by the lithographic apparatus has been measured.Knowing the ratio, and knowing the size of the critical dimensionvariance either side of the maximum for the exposed image, allows thesize of the central maximum caused solely by speckle to be determined.In other words, the critical dimension variance of the holes causedsolely by speckle is determined.

The critical dimension variance of the holes caused by speckle isdetermined in nm². This can be converted to dose variation caused byspeckle, and converted to the number of independent speckle patterns Nof the radiation source in the manner explained above in connection withthe previous embodiment.

FIGS. 22 and 23 depict the results of the same simulation, but this timedisplaying data indicating variation of y-direction position dY of theholes as a function of the separation between the holes (FIG. 22), andvariation of the x-direction position dX as a function of the separationof the holes (FIG. 23). The data obtained from the simulation may beused together with an image formed using a lithographic apparatus todetermine speckle in the same manner as described above in connectionwith critical dimension variation.

Although an embodiment which uses particular parameters such as patternfeature size has been described, it will be appreciated that otherembodiments may be used. In general, a pattern comprising atwo-dimensional array of pattern features which will form a twodimensional array of image features on a substrate may be used. Thepattern may be used in combination with an illumination mode which willgenerate a two-dimensional diffraction pattern comprising an array offeatures. The features of the two-dimensional diffraction pattern mayhave the same pitch and orientation as the imaged pattern features. Thecritical dimension variation of features as correlated with themselvesand as correlated with other features may be analysed to determinespeckle. The positional variation of features as correlated withthemselves and as correlated with other features may be analysed todetermine speckle.

Specific embodiments of methods and apparatus for measuring thecontribution of speckle have been described above with reference to thefigures. However, other embodiments of the invention may be different tothe specific details described above. Whilst embodiments of theinvention have been described above with reference to a lithographicapparatus LA, the invention may be used to determine the contribution ofspeckle in any optical system comprising an illumination systemconfigured to illuminate a patterning device and a projection systemconfigured to project a patterned radiation beam onto an image plane.

FIG. 24 is a flowchart which outlines the steps of a general method formeasuring the effects of speckle in an optical system according anembodiment. At step S1 an illumination system is configured to form aperiodic illumination mode. The periodic illumination mode comprises aspatial intensity profile in a pupil plane of the illumination systemwhich is periodic in at least one direction. For example, the intensityof radiation in the pupil plane may be substantially sinusoidal (e.g., acosine function such as 1+cos(x)) as a function of position in at leastone direction (e.g. an x-direction) in the pupil plane.

The spatial intensity profile in the pupil plane may not be periodic insome directions. For example, the spatial intensity profile may beperiodic in an x-direction but may not be periodic in a y-direction. Thespatial intensity profile may for example follow a Gaussian distributionin the y-direction.

The periodic spatial intensity profile may include K periods in thepupil plane. K may be an integer. K may be an odd number. K may begreater than 2. K may for example be 5 or more. In some embodiments Kmay about 17 or less.

The illumination mode illuminates a patterning device in an opticalsystem. The patterning device imparts the radiation with a pattern,thereby forming a patterned radiation beam. The spatial intensityprofile of radiation in the pupil plane determines the angular intensityprofile of radiation which illuminates the patterning device. Theperiodic spatial intensity profile in the pupil plane will thereforecause the patterning device to be illuminated with a periodic angularintensity profile.

At step S2 a dose of radiation which is received in an image plane ofthe optical system as a function of position in the image plane ismeasured. The patterned radiation beam is projected onto the image planeby a projection system. The patterned radiation beam may, for example,include one or more line features (i.e. a line of radiation). Thereceived dose of radiation may be measured directly or may be measuredindirectly. For example, a substrate may be positioned in the imageplane and may be exposed to the patterned radiation beam. One or morefeatures of the patterned radiation beam may be transferred to thesubstrate by exposure of the substrate to the one or more features. Forexample, a resist may be provided on the substrate. Exposure of theresist to the features of the patterned radiation beam may cause a statechange in the exposed portion of the resist. The resist may bedeveloped, for example, using an etching process so as to form one ormore features of the patterned radiation beam in the resist. Thedeveloped resist may form a mask for etching the feature into thesubstrate so as to transfer the feature into the substrate.

In embodiments in which the feature of the patterned radiation beam istransferred to a substrate. The dose of radiation which is received inthe image plane may be indirectly measured by measuring a dimension ofone or more features in the substrate. For example, the width of afeature in the substrate may be approximately proportional to the doseof radiation which is received at that location in the image plane.Measuring the width of the feature as a function of position on thesubstrate may therefore allow the dose of radiation which is received inthe image plane as a function of position in the image plane to bedetermined.

A dimension of one or more features in a substrate may, for example, bemeasured using a scanning electron microscope. The scanning electronmicroscope may be used to form an image of a feature which is patternedinto the substrate. A dimension of the feature may be measured byperforming image analysis on an image of the feature which is patternedinto the substrate. For example, one or more edges of the feature may bedetected in the image so as to determine the positions of the edges ofthe feature (e.g. the edges of a line feature). The positions of theedges of the feature may be used to determine a dimension of thefeature. For example, the width of a feature may be determined atdifferent positions in the feature. In some embodiments the width of aline feature may be determined at different positions along the lengthof the line. The measured width of the feature as a function of positionon the substrate may allow the dose of radiation which is received inthe image plane as a function of position in the image plane to bedetermined

In some embodiments a plurality of features may be exposed and adimension of the plurality of features may be measured. For example, insome embodiments more than about 100 line features may be exposed andthe line width of each feature may be measured thereby providing morethan about 100 line width series for a given illumination mode. In someembodiments more than about 1000 line features may be exposed in orderto provide more than about 1000 line width series for a givenillumination mode. A plurality of line width series for a givenillumination mode may be used to calculate an average power spectraldensity at a plurality of spatial frequencies for the given illuminationmode.

Apparatus configured to measure a dose of radiation which is received inthe image plane as a function of position on the image plane may beconsidered to be a measurement system. A measurement system may comprisea substrate table configured to hold a substrate in the image plane ofthe projection system so as to receive the patterned radiation beam. Thesubstrate may be provided with a resist. The measurement system mayfurther comprise apparatus configured to develop the resist and transferthe pattern to the substrate as was described above. Apparatus which isconfigured to apply a resist to a substrate and to develop the resistmay be referred to as a track.

The measurement system may further comprise a sensor configured todetect the dimension of a feature in the substrate at differentpositions on the substrate. For example, the measurement system maycomprise a sensor (e.g. a scanning electron microscope) configured toform an image of the feature in the substrate. The measurement systemmay further comprise apparatus (e.g. a controller) configured todetermine a dimension of the feature in the substrate. For example acontroller may process an image to detect the position of one or moreedges of the feature (e.g. the edges of a line feature) and maydetermine a dimension of the feature from the detected positions of theedges. The controller may be further configured to determine a dose ofradiation which is received in the image plane from the determineddimension of the feature.

Exposing features on a substrate and measuring a dimension of theexposed features in order to determine a dose of radiation is merely oneexample of a method for determining a received dose of radiation in animage plane as a function of position in the image plane. In otherembodiments, other methods for measuring a received dose of radiationmay be used. In some embodiments, radiation which is received in animage plane may be measured directly, for example, using a sensorpositioned substantially in the image plane. The sensor may measure thespatial intensity profile of radiation in the image plane at differentpositions in the image plane.

Due to the small size of features of the spatial intensity profile inthe image plane, in some embodiments, a magnified image of the spatialintensity profile in the image plane may be formed in a further imageplane. A sensor may be positioned substantially in the further imageplane and may be configured to measure the magnified image of thespatial intensity profile in the image plane. The sensor may, forexample, comprise a camera.

Apparatus configured to measure a spatial intensity profile of radiationin an image plane may be considered to be an example of a measurementsystem. For example, a measurement system may comprise a sensorconfigured to measure the spatial intensity profile of radiation in theimage plane at different positions in the image plane. In someembodiments a measurement system may comprise one or more opticalelements configured to form a magnified image of the image plane in afurther image plane. The sensor may be positioned substantially in thefurther image plane. The measurement system may further comprise acontroller configured to determine a received dose of radiation atdifferent positions in the image plane.

At step S3 one or more spatial frequencies in the image plane areselected at which a variation in the dose is caused by speckle. The oneor more spatial frequencies at which speckle causes a variation in thedose depends on the period of the periodic intensity profile in thepupil plane of the illumination system. The period of the periodicintensity profile in the pupil plane of the illumination system (orequivalently the number of periods K in the pupil plane) may be used toselect the one or more frequencies. For example equation (2) above maybe used to select the one or more frequencies.

At step S4 a measure of the variation of the dose at the selected one ormore spatial frequencies is determined. The measure of the variation inthe dose is indicative of speckle in the image plane. The measure may,for example, comprise an autocorrelation function of a first series anda second series. The first series may be a measured dimension of afeature of the patterned radiation beam at different positions in theimage plane. The second series may be identical to the first series andthe autocorrelation function between the first and second series may becalculated when the second series is offset relative to the firstseries. The autocorrelation function may be calculated at a positionaloffset between the second series and the first series which is equal tothe inverse of the one of more spatial frequencies selected in step S3.That is the positional offset may be equal to the spatial period atwhich variation in the measured dimension is caused by speckle. Themagnitude of the autocorrelation function at such an offset is anindication of speckle in the image plane.

The spatial frequency which is selected in step S3 may correspond to apositional offset in the autocorrelation function at which a localmaximum is seen. The magnitude of the autocorrelation function at apositional offset corresponding to the frequency selected in step S3 maytherefore be a height of the autocorrelation function at a local maximumin the autocorrelation function.

The spatial frequency which is selected in step S3 may, for example, beselected by finding a local maximum in the autocorrelation function. Thepositional offset at which the local maximum is seen may correspond tothe spatial frequency which is selected. That is the spatial frequencymay be taken to be 1 over the positional offset at which the localmaximum is seen.

References which are made herein to a local maximum are intended torefer to regions in which a function (e.g. an autocorrelation function)reaches a local maximum which is not a maximum of the entire function.References to a local maximum are not therefore intended to include aregion in which the function is at a global maximum (e.g. a centralmaximum). References herein to a central maximum in an autocorrelationfunction are intended to refer to a region of the autocorrelationfunction at which the autocorrelation function is at a global maximum.

The measure of the variation in the dose may be used to derive a measureof the speckle in the image plane which is independent of theillumination mode which is used. The measure of the variation of thedose may, for example, be used to derive the variance (or equivalentlythe standard deviation a) in the measured dose in the image plane whichis caused by speckle. In embodiments in which an autocorrelationfunction is determined using the dimension which is measured in step S2,the variance in the measured dose in the image plane which is caused byspeckle corresponds to the contribution of speckle to the height of theautocorrelation function at a global maximum in the autocorrelationfunction.

In some embodiments the height of the autocorrelation function at alocal maximum in the autocorrelation function may be used to derive thecontribution of speckle to the height of the autocorrelation function ata global maximum in the autocorrelation function. For example a ratiobetween the height of a local maximum and the height of a global maximumin an autocorrelation function which represents the contribution ofspeckle to variation in the measured dose may be determined. Thedetermined ratio may be used to scale the height of a measuredautocorrelation function at a local maximum to find the contribution ofspeckle to the height of a global maximum in the autocorrelationfunction.

One or more of the steps which are shown in FIG. 24 and which aredescribed above may be carried out by a controller. For example, thecontroller CN which is shown in FIG. 1 may carry out one or more of thesteps shown in FIG. 24 and described above.

A controller CN as described herein may, in some embodiments, comprise acomputer. A computer may, for example, include a CPU (central processingunit) which is configured to read and execute instructions stored in avolatile memory which takes the form of a random access memory. Thevolatile memory stores instructions for execution by the CPU and dataused by those instructions.

Embodiments have been described above with reference to a lithographicapparatus LA, which includes an illumination system IL configured toilluminate a patterning device MA so as to form a patterned radiationbeam, and a projection system PL configured to project the patternedradiation beam onto an image plane. However, the apparatus and methodsdescribed herein are applicable to determining the contribution ofspeckle in other optical systems which may not be lithographicapparatuses.

As was described above, forming a patterned radiation beam using apatterning device so as to form pattern features in an image plane andthen measuring a dimension of the pattern features in the image plane ismerely one example of a method for determining a received dose ofradiation in an image plane. In other embodiments no patterning devicemay be used and a received dose of radiation in an image plane may bemeasured as a function of position in the image plane by other suitablemeans.

Whilst the embodiments which are described above refer to measuring areceived dose of radiation in an image plane (typically the plane inwhich a substrate is situated), in other embodiments a received dose ofradiation may be measured in any plane which is an optical conjugate ofan image plane. For example, a received dose of radiation mayalternatively be measured in an object plane of an optical system, wherethe object plane is a conjugate plane of an image plane. An example, ofan object plane in a lithographic system may be a plane in which apatterning device MA is typically situated.

Any plane which is optically conjugate to an image plane (e.g. an objectplane) may be referred to herein as a field plane. Examples of a fieldplane therefore include an image plane (e.g. a plane in which asubstrate W is typically situated) and an object plane (e.g. a plane inwhich a patterning device MA is typically situated). In general, thecontribution of speckle may be determined using the methods describedherein by measuring a dose of radiation which is received in any fieldplane of the optical system as a function of position in the fieldplane. The field plane may, for example, be an image plane or an objectplane of an optical system. Any reference herein to measuring a dose ofradiation in an image plane of an optical system may therefore beequivalently replaced with measuring a dose of radiation in a fieldplane.

In general the inventive concepts disclosed herein may be used todetermine the contribution of speckle in any optical system whichcomprises an illumination system operable to form a periodicillumination mode in a pupil plane of the optical system. The periodicillumination mode in the pupil plane serves to advantageously confinethe effects of speckle to a limited number of spatial frequencies in afield plane of the optical system. This advantageously allows thecontribution of speckle to dose variations in the field plane to beseparated from the contributions of other effects.

A pupil plane of an optical system is a plane which has a Fourierrelationship with a field plane. That is, each spatial point in a pupilplane corresponds with an angle in a corresponding field plane and viceversa.

Aspects of the invention may be implemented in any convenient form. Forexample, the invention may be implemented by appropriate computerprograms which may be carried on appropriate carrier media which may betangible carrier media (e.g. disks) or intangible carrier media (e.g.communications signals). Aspects of the invention may also beimplemented using suitable apparatus which may specifically take theform of programmable computers running computer programs arranged toimplement the invention.

While specific embodiments of the invention have been described above,it will be appreciated that the invention may be practiced otherwisethan as described. The description is not intended to limit theinvention.

1. An optical system comprising: an illumination system configured; toform a periodic illumination mode comprising radiation in a pupil planeof the optical system having a spatial intensity profile which isperiodic in at least one direction; a measurement system configured tomeasure a dose of radiation which is received in a a field plane of theoptical system as a function of position in the field plane; and acontroller configured to: select one or more spatial frequencies in thefield plane at which variation in the received dose of radiation as afunction of position is caused by speckle; and determine a measure ofthe variation of the received dose of radiation as a function ofposition at the selected one or more spatial frequencies, the measure ofthe variation in the received dose being indicative of speckle in thefield plane.
 2. The optical system of claim 2, wherein the illuminationsystem is configured to illuminate a patterning device with a radiationbeam, the patterning device being configured to provide the radiationbeam with a pattern in its cross-section so as to form a patternedradiation beam.
 3. The optical system of claim 1, further comprising aprojection system configured to project a radiation beam onto the fieldplane.
 4. The optical system of claim 1, wherein the controller isfurther configured to determine the contribution of speckle to thevariation in the received dose, the contribution of speckle beingdetermined using the measure of the variation of the received dose atthe selected one or more spatial frequencies.
 5. The optical system ofclaim 4, wherein the determined contribution of speckle to the variationin the received dose comprises a variance of the dose which is caused byspeckle.
 6. The optical system of claim 1, wherein the controller isconfigured to determine, from the measure of the variation of thereceived dose at the selected one or more spatial frequencies, a numberof independent speckle patterns which are received in the field plane ina given period of time.
 7. The optical system of claim 1, wherein themeasurement system comprises: a substrate table configured to hold asubstrate substantially in the field plane so as to expose the substrateto the patterned radiation beam; and a sensor configured to detect adimension of a feature patterned into the substrate at differentpositions on the substrate, the dimension of the feature patterned intothe substrate as a function of position on the substrate providing ameasure of the dose of radiation received in the field plane as afunction of position in the field plane.
 8. The optical system of claim7, wherein the sensor comprises a scanning electron microscopeconfigured to take an image of the feature patterned onto the substrateand a controller configured to detect, from the image, a dimension ofthe feature at different positions on the substrate.
 9. The opticalsystem of claim 7, wherein the measurement system further comprises atrack configured to apply a resist to a substrate and develop the resistafter exposure to a patterned radiation beam so as to transfer a patternto the substrate.
 10. The optical system of claim 1, wherein thecontroller is configured to determine an autocorrelation function of afirst series and a second series, wherein the first series comprises themeasured received dose of radiation in the field plane at differentpositions in the field plane and the second series is the same as thefirst series and offset from the first series by a positional offset.11. The optical system of claim 10, wherein the controller is configuredto evaluate the autocorrelation function at a positional offset which isan inverse of the one or more selected spatial frequencies.
 12. Theoptical system of claim 11, wherein the positional offset which is theinverse of the one or more selected spatial frequencies represents apositional offset at which the autocorrelation function is substantiallyat a local maximum.
 13. The optical system of claim 11, wherein theautocorrelation function evaluated at a positional offset which is theinverse of the one or more selected spatial frequencies provides ameasure of the contribution of speckle to a variation in the receiveddose of radiation as a function of the position in the field plane. 14.The optical system of claim 13, wherein the controller is furtherconfigured to scale the autocorrelation function evaluated at apositional offset which is the inverse of the one or more selectedspatial frequencies and determine the total variance in the receiveddose of radiation in the field plane which is caused by speckle.
 15. Theoptical system of claim 14, wherein the controller is further configuredto: determine a ratio of a local maximum to a global maximum in aspeckle autocorrelation function which corresponds to a variation indose in the field plane which is only caused by speckle; and scale theautocorrelation function evaluated at a positional offset which is theinverse of the one or more selected spatial frequencies according to thedetermined ratio.
 16. The optical system of claim 15, further comprisinga sensor apparatus configured to measure a spatial intensity profile ofthe periodic illumination mode in the pupil plane of the optical system,wherein the controller is configured to determine, from the measuredspatial intensity profile of the periodic illumination mode, the ratioof a local maximum to a global maximum in a speckle autocorrelationfunction, and wherein the speckle autocorrelation function correspondsto a variation in dose in the field plane which is only caused byspeckle.
 17. The optical system of claim 15, wherein the controller isconfigured to perform a simulation of radiation propagating through theoptical system and determine, from the simulation, the ratio of a localmaximum to a global maximum in a speckle autocorrelation function whichcorresponds to a variation in dose in the field plane which is onlycaused by speckle.
 18. The optical system of claim 1, further comprisinga radiation source configured to provide a radiation beam to theillumination system, wherein the radiation source is operable to adjustan adjustable property of the radiation beam so as to change a number ofindependent speckle patterns which are received in the field plane perunit time.
 19. The optical system of claim 18, wherein the radiationsource is configured to provide a pulsed radiation beam to theillumination system and wherein the radiation source is operable toadjust the duration of pulses of radiation which are emitted from theradiation source, thereby changing the number of independent specklepatterns which are received in the field plane per unit time.
 20. Theoptical system of claim 18, wherein for each configuration of theadjustable property of the radiation source, the controller isconfigured to: select one or more spatial frequencies in the field planeat which variation in the received dose of radiation as a function ofposition is caused by speckle; and determine a measure of the variationof the received dose of radiation as a function of position at theselected one or more spatial frequencies, the measure of the variationin the received dose being indicative of speckle in the field plane. 21.The optical system of claim 20, wherein the controller is furtherconfigured to evaluate the measure of the variation in the received doseat a plurality of configurations of the adjustable property of theradiation source, and from the evaluation determine the contribution ofspeckle to the variation of the received dose at each configuration. 22.The optical system of claim 1, wherein the controller is configured toselect the one or more spatial frequencies in the field plane at whichthe variation in the measured dimension is caused by speckle, using thenumber of periods of the spatial intensity distribution in the pupilplane of the optical system.
 23. The optical system of claim 22, whereinthe controller is configured to select the one or more spatialfrequencies in the field plane at which the variation in the measureddimension is caused by speckle by calculating a spatial period P_(S)according to: $P_{S} = \frac{\lambda \; K}{2{NA}}$ where K is thenumber of periods of the spatial intensity distribution in the pupilplane of the optical system, λ is the wavelength of the radiation beamand NA is the numerical aperture of the optical system, wherein the oneor more spatial frequencies in the field plane at which the variation inthe measured dimension is caused by speckle is the inverse of thespatial period P_(S).
 24. The optical system of claim 1, wherein theillumination system comprises an array of mirrors, the mirrors beingadjustable so as to adjust the spatial intensity profile in the pupilplane of the optical system.
 25. The optical system of claim 1, whereinthe illumination system is configured to form a periodic illuminationmode comprising radiation in a pupil plane of the optical system havinga periodic spatial intensity profile in a first direction, wherein theperiodic spatial intensity profile includes K periods.
 26. The opticalsystem of claim 25, wherein the illumination system is configured suchthat the spatial intensity profile substantially follows a Gaussiandistribution in a second direction, wherein the second direction issubstantially perpendicular to the first direction.
 27. The opticalsystem of claim 25, wherein K is an integer.
 28. The optical system ofclaim 27, wherein K is an odd number.
 29. The optical system of claim25, wherein K is 5 or more.
 30. The optical system of claim 25, whereinK is 17 or less.
 31. The optical system of claim 25, wherein theillumination system is configured to form a dipole illumination mode.32. The optical system of claim 1, wherein the optical system comprisesa lithographic apparatus.
 33. The optical system of claim 2, wherein thepatterning device is an attenuating phase shift mask.
 34. A method ofmeasuring speckle in an optical system, the optical system comprising anillumination system configured to condition a radiation beam, the methodcomprising: configuring the illumination system to form a periodicillumination mode, comprising radiation in a pupil plane of the opticalsystem having a spatial intensity profile which is periodic in at leastone direction; measuring a dose of radiation which is received in afield plane of the optical system as a function of position in the fieldplane; selecting one or more spatial frequencies in the field plane atwhich variation in the received dose of radiation as a function ofposition is caused by speckle; and determining a measure of thevariation of the received dose of radiation as a function of position atthe selected one or more spatial frequencies, the measure of thevariation in the dimension being indicative of the speckle in the fieldplane.
 35. A method of measuring speckle in a lithographic apparatus,the method comprising: forming a periodic illumination mode ofradiation; patterning the radiation using a pattern comprising a gratingto create patterned radiation; projecting the patterned radiation onto asubstrate to form an image of the grating; measuring line widthvariation of lines of the imaged grating; and performing atwo-dimensional correlation of the line widths in which lines arecorrelated with themselves and are correlated with other lines of theimage
 36. The method of claim 35, wherein the method further comprisesdetermining a ratio of a local maximum to a central maximum for one ormore lines which were correlated with other lines of the image, andusing that ratio together with a local maximum for lines which werecorrelated with themselves to determine a central maximum caused byspeckle for the lines which were correlated with themselves.
 37. Themethod of claim 36, wherein the method further comprises using apreviously performed calibration to convert the size of the centralmaximum to a measurement of dose variation caused by speckle.
 38. Amethod of measuring speckle in a lithographic apparatus, the methodcomprising: forming a quadrupole illumination mode of radiation;patterning the radiation using a pattern comprising a two-dimensionalarray of features to create patterned radiation; projecting thepatterned radiation onto a substrate to form an image; performing atwo-dimensional correlation of the critical dimension of the imagedpattern features as a function of pattern feature separation;determining a size of the correlation function away from a centralmaximum of the correlation function, and using this together with apreviously obtained ratio to determine the size of a central maximum ofthe correlation function that is caused by speckle.
 39. A method ofmeasuring speckle in a lithographic apparatus, the method comprising:forming a quadrupole illumination mode of radiation; patterning theradiation using a pattern comprising a two-dimensional array of featuresto create patterned radiation; projecting the patterned radiation onto asubstrate to form an image having imaged pattern features; performing atwo-dimensional correlation of the positions of the imaged patternfeatures as a function of pattern feature separation; determining a sizeof the correlation function away from a central maximum of thecorrelation function, and using this together with a previously obtainedratio to determine the size of a central maximum of the correlationfunction that is caused by speckle.
 40. The method of claim 38, whereinthe method further comprises using a previously performed calibration toconvert the size of the central maximum to a measurement of dosevariation caused by speckle.